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@unpublished{ET11,
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@unpublished{GR11,
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@article {Hruslov76,
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@incollection {KhrKot94,
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    SERIES = {Adv. Soviet Math.},
    VOLUME = {19},
     PAGES = {129--180},
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   ADDRESS = {Providence, RI},
      YEAR = {1994},
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@book {Mar86,
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   JOURNAL = {Arch. Rational Mech. Anal.},
  FJOURNAL = {Archive for Rational Mechanics and Analysis},
    VOLUME = {31},
      YEAR = {1968/1969},
     PAGES = {372--379},
      ISSN = {0003-9527},
   MRCLASS = {47.55},
  MRNUMBER = {0233240 (38 \#1562)},
MRREVIEWER = {S. Kantorovitz},
}




@article{Tarama04, 
	author={Tarama, S.},
	title={Analyticity of solutions of the {K}orteweg-de {V}ries equation}, 
	journal={J. Math. Kyoto Univ.},
	volume={44}, 
	year={2004}, 
	number={1},
	pages={1--32},
}



@article {Ven86,
    AUTHOR = {Venakides, Stephanos},
     TITLE = {Long time asymptotics of the {K}orteweg-de {V}ries equation},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {293},
      YEAR = {1986},
    NUMBER = {1},
     PAGES = {411--419},
      ISSN = {0002-9947},
     CODEN = {TAMTAM},
   MRCLASS = {35B40 (35Q20)},
  MRNUMBER = {814929 (87d:35022)},
MRREVIEWER = {Amy Cohen},
       DOI = {10.2307/2000288},
       URL = {http://dx.doi.org/10.2307/2000288},
}


@article {Zhang92,
    AUTHOR = {Zhang, Bing Yu},
     TITLE = {Unique continuation for the {K}orteweg-de {V}ries equation},
   JOURNAL = {SIAM J. Math. Anal.},
  FJOURNAL = {SIAM Journal on Mathematical Analysis},
    VOLUME = {23},
      YEAR = {1992},
    NUMBER = {1},
     PAGES = {55--71},
      ISSN = {0036-1410},
     CODEN = {SJMAAH},
   MRCLASS = {35Q53 (34A55 34L25 35B60)},
  MRNUMBER = {1145162 (92k:35252)},
MRREVIEWER = {Mehmet Can},
       DOI = {10.1137/0523004},
       URL = {http://dx.doi.org/10.1137/0523004},
}



%-----from thesis----

@book{PS01,
	Address = {London},
	editor = {E. Roy Pike and Pierre C\'elestin Sabatier},
	Publisher = {Academic Press},
	title = {Scattering: Scattering and Inverse Scattering in Pure and Applied Science},
	Year = {2001},
	pages={1831}
}

@book {Teschl,
    AUTHOR = {Teschl, Gerald},
     TITLE = {Mathematical methods in quantum mechanics},
    SERIES = {Graduate Studies in Mathematics},
    VOLUME = {99},
      NOTE = {With applications to Schr{\"o}dinger operators},
 PUBLISHER = {American Mathematical Society},
   ADDRESS = {Providence, RI},
      YEAR = {2009},
     PAGES = {xiv+305},
      ISBN = {978-0-8218-4660-5},
   MRCLASS = {81-01 (47N50 81Qxx)},
  MRNUMBER = {2499016 (2010h:81002)},
MRREVIEWER = {Rupert L. Frank},
}



@incollection{AK01,
	author = {Tuncay Aktosun and Martin Klaus},
	chapter={2.2.4.},  
	title = {Inverse theory: problem on the line},
	crossref={PS01},
	pages={770--785}
}


@preamble{
   "\def\cprime{$'$} "
}
@article {Burr,
    AUTHOR = {Burridge, Robert},
     TITLE = {The {G}el\cprime fand-{L}evitan, the {M}archenko, and the
              {G}opinath-{S}ondhi integral equations of inverse scattering
              theory, regarded in the context of inverse impulse-response
              problems},
   JOURNAL = {Wave Motion},
  FJOURNAL = {Wave Motion},
    VOLUME = {2},
      YEAR = {1980},
    NUMBER = {4},
     PAGES = {305--323},
      ISSN = {0165-2125},
     CODEN = {WAMOD9},
   MRCLASS = {81F99 (35Q20 86A15)},
  MRNUMBER = {593133 (82d:81144)},
       DOI = {10.1016/0165-2125(80)90011-6},
       URL = {http://dx.doi.org/10.1016/0165-2125(80)90011-6},
}
	

@article {Fad,
   author = {Faddeev, Lyudvig Dmitrievich},
   title = {Inverse problem of quantum scattering theory. II.},
   journal = {Journal of Mathematical Sciences},
   publisher = {Springer New York},
   issn = {1072-3374},
   keyword = {Mathematics and Statistics},
   pages = {334-396},
   volume = {5},
   issue = {3},
   url = {http://dx.doi.org/10.1007/BF01083780},
   note = {10.1007/BF01083780},
   year = {1976}
}

@article {AKM93,
    AUTHOR = {Aktosun, Tuncay and Klaus, Martin and van der Mee, Cornelis},
     TITLE = {On the {R}iemann-{H}ilbert problem for the one-dimensional
              {S}chr\"odinger equation},
   JOURNAL = {J. Math. Phys.},
  FJOURNAL = {Journal of Mathematical Physics},
    VOLUME = {34},
      YEAR = {1993},
    NUMBER = {7},
     PAGES = {2651--2690},
      ISSN = {0022-2488},
     CODEN = {JMAPAQ},
   MRCLASS = {34L25 (34A55 34L40 81Q05)},
  MRNUMBER = {1224170 (95f:34130)},
       DOI = {10.1063/1.530089},
       URL = {http://dx.doi.org/10.1063/1.530089},
}

@article {Akt96,
    AUTHOR = {Aktosun, Tuncay},
     TITLE = {Inverse {S}chr\"odinger scattering on the line with partial
              knowledge of the potential},
   JOURNAL = {SIAM J. Appl. Math.},
  FJOURNAL = {SIAM Journal on Applied Mathematics},
    VOLUME = {56},
      YEAR = {1996},
    NUMBER = {1},
     PAGES = {219--231},
      ISSN = {0036-1399},
     CODEN = {SMJMAP},
   MRCLASS = {81U40 (34A55 34C25)},
  MRNUMBER = {1372897 (96m:81250)},
MRREVIEWER = {Ricardo Weder},
       DOI = {10.1137/S0036139994273995},
       URL = {http://dx.doi.org/10.1137/S0036139994273995},
}

@article {AS00,
    AUTHOR = {Aktosun, Tuncay and Sacks, Paul E.},
     TITLE = {Inversion of reflectivity data for nondecaying potentials},
   JOURNAL = {SIAM J. Appl. Math.},
  FJOURNAL = {SIAM Journal on Applied Mathematics},
    VOLUME = {60},
      YEAR = {2000},
    NUMBER = {4},
     PAGES = {1340--1356 (electronic)},
      ISSN = {0036-1399},
   MRCLASS = {81U40 (34A55 34L25)},
  MRNUMBER = {1760038 (2001b:81156)},
MRREVIEWER = {Cornelis van der Mee},
       DOI = {10.1137/S0036139999355588},
       URL = {http://dx.doi.org/10.1137/S0036139999355588},
}

@article {AMR07,
    AUTHOR = {Avdonin, Sergei and Mikhaylov, Victor and Rybkin, Alexei},
     TITLE = {The boundary control approach to the {T}itchmarsh-{W}eyl
              {$m$}-function. {I}. {T}he response operator and the
              {$A$}-amplitude},
   JOURNAL = {Comm. Math. Phys.},
  FJOURNAL = {Communications in Mathematical Physics},
    VOLUME = {275},
      YEAR = {2007},
    NUMBER = {3},
     PAGES = {791--803},
      ISSN = {0010-3616},
     CODEN = {CMPHAY},
   MRCLASS = {93B51 (34L40 35J10 47E05 93C20)},
  MRNUMBER = {2336364 (2008g:93083)},
MRREVIEWER = {Louis Roder Tcheugou{\'e} T{\'e}bou},
       DOI = {10.1007/s00220-007-0315-2},
       URL = {http://dx.doi.org/10.1007/s00220-007-0315-2},
}

@article {BSL95,
    AUTHOR = {Braun, M. and Sofianos, S. A. and Lipperheide, R.},
     TITLE = {One-dimensional {M}archenko inversion in the presence of bound
              states},
   JOURNAL = {Inverse Problems},
  FJOURNAL = {Inverse Problems. An International Journal on the Theory and
              Practice of Inverse Problems, Inverse Methods and Computerized
              Inversion of Data},
    VOLUME = {11},
      YEAR = {1995},
    NUMBER = {3},
     PAGES = {L1--L3},
      ISSN = {0266-5611},
     CODEN = {INPEEY},
   MRCLASS = {81U40 (34A55 34L25)},
  MRNUMBER = {1333092 (96c:81235)},
MRREVIEWER = {Fran{\c{c}}ois Nicoleau},
       URL = {http://stacks.iop.org/0266-5611/11/1},
}

@article {BusFo,
    AUTHOR = {Buslaev, V. and Fomin, V.},
     TITLE = {An inverse scattering problem for the one-dimensional
              {S}chr\"odinger equation on the entire axis},
   JOURNAL = {Vestnik Leningrad. Univ.},
  FJOURNAL = {Vestnik Leningrad University. Mathematics},
    VOLUME = {17},
      YEAR = {1962},
    NUMBER = {1},
     PAGES = {56--64},
      ISSN = {0146-924x},
   MRCLASS = {81.34},
  MRNUMBER = {0139371 (25 \#2804)},
}

@article {CoKap,
    AUTHOR = {Cohen, Amy and Kappeler, Thomas},
     TITLE = {Scattering and inverse scattering for steplike potentials in
              the {S}chr\"odinger equation},
   JOURNAL = {Indiana Univ. Math. J.},
  FJOURNAL = {Indiana University Mathematics Journal},
    VOLUME = {34},
      YEAR = {1985},
    NUMBER = {1},
     PAGES = {127--180},
      ISSN = {0022-2518},
     CODEN = {IUMJAB},
   MRCLASS = {34B25 (34A55 81F05)},
  MRNUMBER = {773398 (86k:34017)},
MRREVIEWER = {M. S. Agranovich},
       DOI = {10.1512/iumj.1985.34.34008},
       URL = {http://dx.doi.org/10.1512/iumj.1985.34.34008},
}


@book {Eck,
    AUTHOR = {Eckhaus, Wiktor and van Harten, Aart},
     TITLE = {The inverse scattering transformation and the theory of
              solitons},
    SERIES = {North-Holland Mathematics Studies},
    VOLUME = {50},
      NOTE = {An introduction},
 PUBLISHER = {North-Holland Publishing Co.},
   ADDRESS = {Amsterdam},
      YEAR = {1981},
     PAGES = {xi+222},
      ISBN = {0-444-86166-1},
   MRCLASS = {35Q20 (34B25 76B25 81C05 81F99)},
  MRNUMBER = {615557 (83c:35101)},
MRREVIEWER = {M. S. Agranovich},
}




@article {GH94,
    AUTHOR = {Gesztesy, Fritz and Holden, Helge},
     TITLE = {Trace formulas and conservation laws for nonlinear evolution
              equations},
   JOURNAL = {Rev. Math. Phys.},
  FJOURNAL = {Reviews in Mathematical Physics. A Journal for Both Review and
              Original Research Papers in the Field of Mathematical Physics},
    VOLUME = {6},
      YEAR = {1994},
    NUMBER = {1},
     PAGES = {51--95},
      ISSN = {0129-055X},
   MRCLASS = {35Q53 (34A55 34L25 35Q55 58F07)},
  MRNUMBER = {1263198 (95h:35198a)},
MRREVIEWER = {Vladimir V. Sukhanov},
       DOI = {10.1142/S0129055X94000055},
       URL = {http://dx.doi.org/10.1142/S0129055X94000055},
}


@article {GS'00,
    AUTHOR = {Gesztesy, Fritz and Simon, Barry},
     TITLE = {A new approach to inverse spectral theory. {II}. {G}eneral
              real potentials and the connection to the spectral measure},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {152},
      YEAR = {2000},
    NUMBER = {2},
     PAGES = {593--643},
      ISSN = {0003-486X},
     CODEN = {ANMAAH},
   MRCLASS = {34L05 (34A55 34B24 47E05)},
  MRNUMBER = {1804532 (2001m:34185b)},
MRREVIEWER = {Paul E. Sacks},
       DOI = {10.2307/2661393},
       URL = {http://dx.doi.org/10.2307/2661393},
}

@article {GW95,
    AUTHOR = {Gr{\'e}bert, Beno{\^{\i}}t and Weder, Ricardo},
     TITLE = {Reconstruction of a potential on the line that is a priori
              known on the half line},
   JOURNAL = {SIAM J. Appl. Math.},
  FJOURNAL = {SIAM Journal on Applied Mathematics},
    VOLUME = {55},
      YEAR = {1995},
    NUMBER = {1},
     PAGES = {242--254},
      ISSN = {0036-1399},
     CODEN = {SMJMAP},
   MRCLASS = {34L25 (34A55 81U40)},
  MRNUMBER = {1313016 (95j:34122)},
MRREVIEWER = {Carol Shubin},
       DOI = {10.1137/S0036139993254656},
       URL = {http://dx.doi.org/10.1137/S0036139993254656},
}



@incollection {Ramm,
    AUTHOR = {Ramm, A. G.},
     TITLE = {Property {C} for {ODE} and applications to inverse problems},
 BOOKTITLE = {Operator theory and its applications ({W}innipeg, {MB}, 1998)},
    SERIES = {Fields Inst. Commun.},
    VOLUME = {25},
     PAGES = {15--75},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {2000},
   MRCLASS = {34B24 (34A55 34L25 35R30 47E05 74J25 81U40)},
  MRNUMBER = {1759536 (2001f:34048)},
MRREVIEWER = {Vyacheslav N. Pivovarchik},
}

@article {RS94,
    AUTHOR = {Rundell, William and Sacks, Paul},
     TITLE = {On the determination of potentials without bound state data},
   JOURNAL = {J. Comput. Appl. Math.},
  FJOURNAL = {Journal of Computational and Applied Mathematics},
    VOLUME = {55},
      YEAR = {1994},
    NUMBER = {3},
     PAGES = {325--347},
      ISSN = {0377-0427},
     CODEN = {JCAMDI},
   MRCLASS = {81U40 (34A55 34L25 81-08)},
  MRNUMBER = {1329878 (96d:81217)},
MRREVIEWER = {Ghias Hachem},
       DOI = {10.1016/0377-0427(94)90037-X},
       URL = {http://dx.doi.org/10.1016/0377-0427(94)90037-X},
}

@article {RybIP09,
    AUTHOR = {Rybkin, Alexei},
     TITLE = {On the {M}archenko inverse scattering procedure with partial
              information on the potential},
   JOURNAL = {Inverse Problems},
  FJOURNAL = {Inverse Problems. An International Journal on the Theory and
              Practice of Inverse Problems, Inverse Methods and Computerized
              Inversion of Data},
    VOLUME = {25},
      YEAR = {2009},
    NUMBER = {9},
     PAGES = {095011, 34},
      ISSN = {0266-5611},
     CODEN = {INPEEY},
   MRCLASS = {35R30 (35P25 78A40)},
  MRNUMBER = {2540891 (2011a:35581)},
       DOI = {10.1088/0266-5611/25/9/095011},
       URL = {http://dx.doi.org/10.1088/0266-5611/25/9/095011},
}

@article {Simon99,
    AUTHOR = {Simon, Barry},
     TITLE = {A new approach to inverse spectral theory. {I}. {F}undamental
              formalism},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {150},
      YEAR = {1999},
    NUMBER = {3},
     PAGES = {1029--1057},
      ISSN = {0003-486X},
     CODEN = {ANMAAH},
   MRCLASS = {34L05 (34A55 34B24 47E05)},
  MRNUMBER = {1740987 (2001m:34185a)},
MRREVIEWER = {Paul E. Sacks},
       DOI = {10.2307/121061},
       URL = {http://dx.doi.org/10.2307/121061},
}

@book {Simon05,
    AUTHOR = {Simon, Barry},
     TITLE = {Trace ideals and their applications},
    SERIES = {Mathematical Surveys and Monographs},
    VOLUME = {120},
   EDITION = {Second},
 PUBLISHER = {American Mathematical Society},
   ADDRESS = {Providence, RI},
      YEAR = {2005},
     PAGES = {viii+150},
      ISBN = {0-8218-3581-5},
   MRCLASS = {47L20 (47A40 47A55 47B10 47B36 47E05 81Q15 81U99)},
  MRNUMBER = {2154153 (2006f:47086)},
MRREVIEWER = {Pavel B. Kurasov},
}

%Snieder, R., and J. Trampert, Inverse problems in geophysics, in Wavefield inversion, edited by A. Wirgin, pp. 119-190, Springer Verlag, New York, 1999 

@INCOLLECTION{ST99,
  author = {Snieder, Roel and Trampert, Jeannot},
  title = {Inverse Problems in Geophysics},
  booktitle = {Wavefield inversion },
  publisher = {Springer Verlag},
  year = {1999},
  editor = {Wirgin, A.},
  pages = {119-190},
  address = {New York}
}


@book {Titch,
    	AUTHOR = {Titchmarsh, Edward Charles},
     	TITLE = {Eigenfunction expansions associated with second-order
              differential equations. {P}art {I}},
   % SERIES = {Second Edition}, % I have an earlier edition, different year, pages, not sure about mr
 	PUBLISHER = {Clarendon Press},
	address= {Oxford},
     	YEAR = {1950},
     PAGES = {184},
   %MRCLASS = {34.30},
  %MRNUMBER = {0176151 (31 \#426)},
}

@article {Weidl,
    AUTHOR = {Weidl, Timo},
     TITLE = {On the {L}ieb-{T}hirring constants {$L\sb {\gamma,1}$} for
              {$\gamma\geq 1/2$}},
   JOURNAL = {Comm. Math. Phys.},
  FJOURNAL = {Communications in Mathematical Physics},
    VOLUME = {178},
      YEAR = {1996},
    NUMBER = {1},
     PAGES = {135--146},
      ISSN = {0010-3616},
     CODEN = {CMPHAY},
   MRCLASS = {81Q10},
  MRNUMBER = {1387945 (97c:81039)},
MRREVIEWER = {Liu Yang},
       URL = {http://projecteuclid.org/getRecord?id=euclid.cmp/1104286558},
}

@unpublished{Ry11,
	author={Alexei Rybkin},
	title={The {H}irota {$\tau $}-function and well-posedness of the {K}d{V} equation with an arbitrary step like initial profile decaying on the right half line},
	year={2011},
	note={To appear in Nonlinearity},
	eprint={arXiv:1012.0052v1}
	url={http://arxiv.org/PS_cache/arxiv/pdf/1012/1012.0052v1.pdf}
}


% from MR for ffavr

@article {MR2336364,
    AUTHOR = {Avdonin, Sergei and Mikhaylov, Victor and Rybkin, Alexei},
     TITLE = {The boundary control approach to the {T}itchmarsh-{W}eyl
              {$m$}-function. {I}. {T}he response operator and the
              {$A$}-amplitude},
   JOURNAL = {Comm. Math. Phys.},
  FJOURNAL = {Communications in Mathematical Physics},
    VOLUME = {275},
      YEAR = {2007},
    NUMBER = {3},
     PAGES = {791--803},
      ISSN = {0010-3616},
     CODEN = {CMPHAY},
   MRCLASS = {93B51 (34L40 35J10 47E05 93C20)},
  MRNUMBER = {2336364 (2008g:93083)},
MRREVIEWER = {Louis Roder Tcheugou{\'e} T{\'e}bou},
       DOI = {10.1007/s00220-007-0315-2},
       URL = {http://dx.doi.org/10.1007/s00220-007-0315-2},
}

@article {MR1982789,
    AUTHOR = {Belov, S. M. and Rybkin, A. V.},
     TITLE = {Higher order trace formulas of the {B}uslaev-{F}addeev-type
              for the half-line {S}chr\"odinger operator with long-range
              potentials},
   JOURNAL = {J. Math. Phys.},
  FJOURNAL = {Journal of Mathematical Physics},
    VOLUME = {44},
      YEAR = {2003},
    NUMBER = {7},
     PAGES = {2748--2761},
      ISSN = {0022-2488},
     CODEN = {JMAPAQ},
   MRCLASS = {81U05 (34L25 47E05 81Q10)},
  MRNUMBER = {1982789 (2004g:81299)},
       DOI = {10.1063/1.1579549},
       URL = {http://dx.doi.org/10.1063/1.1579549},
}

@article {MR2026899,
    AUTHOR = {Belov, Sergei and Rybkin, Alexei},
     TITLE = {On the existence of {WKB}-type asymptotics for the generalized
              eigenvectors of discrete string operators},
   JOURNAL = {Bull. London Math. Soc.},
  FJOURNAL = {The Bulletin of the London Mathematical Society},
    VOLUME = {36},
      YEAR = {2004},
    NUMBER = {2},
     PAGES = {241--251},
      ISSN = {0024-6093},
     CODEN = {LMSBBT},
   MRCLASS = {47B36 (39A70)},
  MRNUMBER = {2026899 (2005d:47050)},
MRREVIEWER = {Stanislav Kupin},
       DOI = {10.1112/S0024609303002819},
       URL = {http://dx.doi.org/10.1112/S0024609303002819},
}

@article {MR721313,
    AUTHOR = {Rybkin, A. V.},
     TITLE = {Trace formulas for resonances},
   JOURNAL = {Teoret. Mat. Fiz.},
  FJOURNAL = {Akademiya Nauk SSSR. Teoreticheskaya i Matematicheskaya
              Fizika},
    VOLUME = {56},
      YEAR = {1983},
    NUMBER = {3},
     PAGES = {439--447},
      ISSN = {0564-6162},
   MRCLASS = {35P25 (34B25 47F05 78A45)},
  MRNUMBER = {721313 (84k:35110)},
}

@article {MR764904,
    AUTHOR = {Rybkin, A. V.},
     TITLE = {The spectral shift function for a dissipative and a
              selfadjoint operator, and trace formulas for resonances},
   JOURNAL = {Mat. Sb. (N.S.)},
  FJOURNAL = {Matematicheski\u\i\ Sbornik. Novaya Seriya},
    VOLUME = {125(167)},
      YEAR = {1984},
    NUMBER = {3},
     PAGES = {420--430},
      ISSN = {0368-8666},
   MRCLASS = {47A40},
  MRNUMBER = {764904 (86j:47011b)},
MRREVIEWER = {Hagen Neidhardt},
}

@article {MR776963,
    AUTHOR = {Rybkin, A. V.},
     TITLE = {The trace formula for dissipative and selfadjoint operators
              and spectral identities for resonances},
   JOURNAL = {Vestnik Leningrad. Univ. Mat. Mekh. Astronom.},
  FJOURNAL = {Vestnik Leningradskogo Universiteta. Matematika, Mekhanika,
              Astronomiya},
      YEAR = {1984},
    NUMBER = {vyp. 4},
     PAGES = {97--99, 112},
      ISSN = {0024-0850},
   MRCLASS = {47A40},
  MRNUMBER = {776963 (86j:47011a)},
MRREVIEWER = {Hagen Neidhardt},
}

@preamble{
   "\def\cprime{$'$} "
}
@article {MR925084,
    AUTHOR = {Rybkin, A. V.},
     TITLE = {A trace formula for a contractive and a unitary operator},
   JOURNAL = {Funktsional. Anal. i Prilozhen.},
  FJOURNAL = {Akademiya Nauk SSSR. Funktsional\cprime ny\u\i\ Analiz i ego
              Prilozheniya},
    VOLUME = {21},
      YEAR = {1987},
    NUMBER = {4},
     PAGES = {85--87},
      ISSN = {0374-1990},
   MRCLASS = {47A55 (47A40 47B10)},
  MRNUMBER = {925084 (89e:47014)},
MRREVIEWER = {Hagen Neidhardt},
}

@preamble{
   "\def\cprime{$'$} "
}
@article {MR1027002,
    AUTHOR = {Rybkin, A. V.},
     TITLE = {The discrete and the singular spectrum in the trace formula
              for a contractive and a unitary operator},
   JOURNAL = {Funktsional. Anal. i Prilozhen.},
  FJOURNAL = {Akademiya Nauk SSSR. Funktsional\cprime ny\u\i\ Analiz i ego
              Prilozheniya},
    VOLUME = {23},
      YEAR = {1989},
    NUMBER = {3},
     PAGES = {84--85},
      ISSN = {0374-1990},
   MRCLASS = {47A10 (47A40 47A55 47B44)},
  MRNUMBER = {1027002 (90k:47010)},
MRREVIEWER = {Hagen Neidhardt},
       DOI = {10.1007/BF01079541},
       URL = {http://dx.doi.org/10.1007/BF01079541},
}

@article {MR1010000,
    AUTHOR = {Rybkin, A. V.},
     TITLE = {Convergence of arguments of {B}laschke products in {$L\sb
              p$}-metrics},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {111},
      YEAR = {1991},
    NUMBER = {3},
     PAGES = {701--708},
      ISSN = {0002-9939},
     CODEN = {PAMYAR},
   MRCLASS = {30D50 (30E25)},
  MRNUMBER = {1010000 (91f:30046)},
MRREVIEWER = {C. N. Linden},
       DOI = {10.2307/2048407},
       URL = {http://dx.doi.org/10.2307/2048407},
}

@article {MR1045149,
    AUTHOR = {Rybkin, Alexey V.},
     TITLE = {On the evaluation of spectral projections onto absolutely
              continuous parts of a contraction},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {112},
      YEAR = {1991},
    NUMBER = {2},
     PAGES = {451--455},
      ISSN = {0002-9939},
     CODEN = {PAMYAR},
   MRCLASS = {47A30 (47A20 47A45)},
  MRNUMBER = {1045149 (91i:47011)},
MRREVIEWER = {E. Durszt},
       DOI = {10.2307/2048739},
       URL = {http://dx.doi.org/10.2307/2048739},
}

@article {MR1148973,
    AUTHOR = {Rybkin, A. V.},
     TITLE = {The {S}tieltjes {$B$}-integral and the summation of spectral
              decompositions of some classes of contraction operators},
   JOURNAL = {Dokl. Akad. Nauk SSSR},
  FJOURNAL = {Doklady Akademii Nauk SSSR},
    VOLUME = {319},
      YEAR = {1991},
    NUMBER = {3},
     PAGES = {562--566},
      ISSN = {0002-3264},
   MRCLASS = {47A45 (47A60)},
  MRNUMBER = {1148973 (92k:47024)},
MRREVIEWER = {F.-H. Vasilescu},
}

@article {MR1203220,
    AUTHOR = {Rybkin, A. V.},
     TITLE = {Functional calculus for contractions with an absolutely
              continuous spectrum, and an operator-valued {C}arleson
              measure},
   JOURNAL = {Dokl. Akad. Nauk},
  FJOURNAL = {Rossi\u\i skaya Akademiya Nauk. Doklady Akademii Nauk},
    VOLUME = {326},
      YEAR = {1992},
    NUMBER = {3},
     PAGES = {417--420},
      ISSN = {0869-5652},
   MRCLASS = {47A45 (47A60)},
  MRNUMBER = {1203220 (94b:47018)},
MRREVIEWER = {Hari Bercovici},
}

@article {MR1215164,
    AUTHOR = {Rybkin, A. V.},
     TITLE = {Duality of {L}ipschitz and {B}esov classes, and the
              {S}tieltjes {$B$}-integral},
   JOURNAL = {Mat. Zametki},
  FJOURNAL = {Rossi\u\i skaya Akademiya Nauk. Matematicheskie Zametki},
    VOLUME = {53},
      YEAR = {1993},
    NUMBER = {1},
     PAGES = {104--110, 156},
      ISSN = {0025-567X},
   MRCLASS = {46E30},
  MRNUMBER = {1215164 (94d:46034)},
MRREVIEWER = {Lubo{\v{s}} Pick},
       DOI = {10.1007/BF01208526},
       URL = {http://dx.doi.org/10.1007/BF01208526},
}

@article {MR1309184,
    AUTHOR = {Rybkin, A. V.},
     TITLE = {The spectral shift function, the characteristic function of a
              contraction and a generalized integral},
   JOURNAL = {Mat. Sb.},
  FJOURNAL = {Rossi\u\i skaya Akademiya Nauk. Matematicheski\u\i\ Sbornik},
    VOLUME = {185},
      YEAR = {1994},
    NUMBER = {10},
     PAGES = {91--144},
      ISSN = {0368-8666},
   MRCLASS = {47-02 (47A40 47A45 47A55 47B99)},
  MRNUMBER = {1309184 (96k:47002)},
MRREVIEWER = {Sergei Naboko},
       DOI = {10.1070/SM1995v083n01ABEH003589},
       URL = {http://dx.doi.org/10.1070/SM1995v083n01ABEH003589},
}

@article {MR1390661,
    AUTHOR = {Rybkin, A. V.},
     TITLE = {On {$A$}-integrability of the spectral shift function of
              unitary operators arising in the {L}ax-{P}hillips scattering
              theory},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {83},
      YEAR = {1996},
    NUMBER = {3},
     PAGES = {683--699},
      ISSN = {0012-7094},
     CODEN = {DUMJAO},
   MRCLASS = {58G25},
  MRNUMBER = {1390661 (97e:58224)},
MRREVIEWER = {Hiroshi Isozaki},
       DOI = {10.1215/S0012-7094-96-08322-2},
       URL = {http://dx.doi.org/10.1215/S0012-7094-96-08322-2},
}

@article {MR1674653,
    AUTHOR = {Rybkin, Alexei},
     TITLE = {On a trace formula of the {B}uslaev-{F}addeev type for a
              long-range potential},
   JOURNAL = {J. Math. Phys.},
  FJOURNAL = {Journal of Mathematical Physics},
    VOLUME = {40},
      YEAR = {1999},
    NUMBER = {3},
     PAGES = {1334--1343},
      ISSN = {0022-2488},
     CODEN = {JMAPAQ},
   MRCLASS = {34L40 (34L25 47A55 47E05 81Q10)},
  MRNUMBER = {1674653 (99k:34188)},
MRREVIEWER = {Mayumi Ohmiya},
       DOI = {10.1063/1.532805},
       URL = {http://dx.doi.org/10.1063/1.532805},
}

@article {MR1773534,
    AUTHOR = {Rybkin, V. A. and Yazenin, A. V.},
     TITLE = {On strong stability in problems of probabilistic optimization},
   JOURNAL = {Izv. Akad. Nauk Teor. Sist. Upr.},
  FJOURNAL = {Rossi\u\i skaya Akademiya Nauk. Izvestiya Akademii Nauk.
              Teoriya i Sistemy Upravleniya},
      YEAR = {2000},
    NUMBER = {2},
     PAGES = {90--95},
      ISSN = {0002-3388},
   MRCLASS = {90C70 (90C31)},
  MRNUMBER = {1773534 (2001c:90111)},
}

@article {MR1812460,
    AUTHOR = {Rybkin, Alexei},
     TITLE = {On an analogue of {C}auchy's formula for {$H\sp p,1/2\leq
              p<1$}, and the {C}auchy type integral of a singular
              measure},
   JOURNAL = {Complex Variables Theory Appl.},
  FJOURNAL = {Complex Variables. Theory and Application. An International
              Journal},
    VOLUME = {43},
      YEAR = {2000},
    NUMBER = {2},
     PAGES = {139--149},
      ISSN = {0278-1077},
     CODEN = {CVTADV},
   MRCLASS = {30E20 (26A39 30D55)},
  MRNUMBER = {1812460 (2001i:30042)},
}

@article {MR1799418,
    AUTHOR = {Rybkin, Alexei},
     TITLE = {Kd{V} invariants and {H}erglotz functions},
   JOURNAL = {Differential Integral Equations},
  FJOURNAL = {Differential and Integral Equations. An International Journal
              for Theory \& Applications},
    VOLUME = {14},
      YEAR = {2001},
    NUMBER = {4},
     PAGES = {493--512},
      ISSN = {0893-4983},
   MRCLASS = {34L40 (35C05 35Q53)},
  MRNUMBER = {1799418 (2001k:34155)},
MRREVIEWER = {Vyacheslav N. Pivovarchik},
}

@article {MR1856247,
    AUTHOR = {Rybkin, Alexei},
     TITLE = {On the trace approach to the inverse scattering problem in
              dimension one},
   JOURNAL = {SIAM J. Math. Anal.},
  FJOURNAL = {SIAM Journal on Mathematical Analysis},
    VOLUME = {32},
      YEAR = {2001},
    NUMBER = {6},
     PAGES = {1248--1264 (electronic)},
      ISSN = {0036-1410},
   MRCLASS = {34L25 (34A55 34L40 47E05)},
  MRNUMBER = {1856247 (2002f:34201)},
MRREVIEWER = {P. A. Mishnayevskiy},
       DOI = {10.1137/S0036141000365620},
       URL = {http://dx.doi.org/10.1137/S0036141000365620},
}

@article {MR1855620,
    AUTHOR = {Rybkin, Alexei},
     TITLE = {On a complete analysis of high-energy scattering matrix
              asymptotics for one dimensional {S}chr\"odinger operators with
              integrable potentials},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {130},
      YEAR = {2002},
    NUMBER = {1},
     PAGES = {59--67 (electronic)},
      ISSN = {0002-9939},
     CODEN = {PAMYAR},
   MRCLASS = {34L25 (34L40 81U05)},
  MRNUMBER = {1855620 (2002g:34193)},
       DOI = {10.1090/S0002-9939-01-06014-2},
       URL = {http://dx.doi.org/10.1090/S0002-9939-01-06014-2},
}

@article {MR1866429,
    AUTHOR = {Rybkin, Alexei},
     TITLE = {Some new and old asymptotic representations of the {J}ost
              solution and the {W}eyl {$m$}-function for {S}chr\"odinger
              operators on the line},
   JOURNAL = {Bull. London Math. Soc.},
  FJOURNAL = {The Bulletin of the London Mathematical Society},
    VOLUME = {34},
      YEAR = {2002},
    NUMBER = {1},
     PAGES = {61--72},
      ISSN = {0024-6093},
     CODEN = {LMSBBT},
   MRCLASS = {34L40 (34L25 81U05)},
  MRNUMBER = {1866429 (2002j:34149)},
MRREVIEWER = {Christian Remling},
       DOI = {10.1112/S0024609301008645},
       URL = {http://dx.doi.org/10.1112/S0024609301008645},
}

@article {MR1929041,
    AUTHOR = {Rybkin, Alexei},
     TITLE = {Necessary and sufficient conditions for absolute summability
              of the trace formulas for certain one dimensional
              {S}chr\"odinger operators},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {131},
      YEAR = {2003},
    NUMBER = {1},
     PAGES = {219--229 (electronic)},
      ISSN = {0002-9939},
     CODEN = {PAMYAR},
   MRCLASS = {34L40 (34L25 47E05)},
  MRNUMBER = {1929041 (2003g:34187)},
MRREVIEWER = {L. V. Kritskov},
       DOI = {10.1090/S0002-9939-02-06555-3},
       URL = {http://dx.doi.org/10.1090/S0002-9939-02-06555-3},
}

@article {MR2043835,
    AUTHOR = {Rybkin, Alexei},
     TITLE = {On the absolutely continuous and negative discrete spectra of
              {S}chr\"odinger operators on the line with locally integrable
              globally square summable potentials},
   JOURNAL = {J. Math. Phys.},
  FJOURNAL = {Journal of Mathematical Physics},
    VOLUME = {45},
      YEAR = {2004},
    NUMBER = {4},
     PAGES = {1418--1425},
      ISSN = {0022-2488},
     CODEN = {JMAPAQ},
   MRCLASS = {34L40 (47E05 81Q10)},
  MRNUMBER = {2043835 (2005e:34261)},
MRREVIEWER = {Mikl{\'o}s Horv{\'a}th},
       DOI = {10.1063/1.1650048},
       URL = {http://dx.doi.org/10.1063/1.1650048},
}

@incollection {MR2103376,
    AUTHOR = {Rybkin, Alexei},
     TITLE = {On a transformation of the {S}turm-{L}iouville equation with
              slowly decaying potentials and the {T}itchmarsh-{W}eyl
              {$m$}-function},
 BOOKTITLE = {Spectral methods for operators of mathematical physics},
    SERIES = {Oper. Theory Adv. Appl.},
    VOLUME = {154},
     PAGES = {185--201},
 PUBLISHER = {Birkh\"auser},
   ADDRESS = {Basel},
      YEAR = {2004},
   MRCLASS = {34E10 (34B20 34E20 34L40 47E05)},
  MRNUMBER = {2103376 (2005h:34147)},
MRREVIEWER = {Stanislav Kupin},
}

@article {MR2194033,
    AUTHOR = {Rybkin, Alexei},
     TITLE = {On the spectral {$L\sb 2$} conjecture,
              {$3/2$}-{L}ieb-{T}hirring inequality and distributional
              potentials},
   JOURNAL = {J. Math. Phys.},
  FJOURNAL = {Journal of Mathematical Physics},
    VOLUME = {46},
      YEAR = {2005},
    NUMBER = {12},
     PAGES = {123505, 8},
      ISSN = {0022-2488},
     CODEN = {JMAPAQ},
   MRCLASS = {81Q10 (34L40 47A55 47B25 47E05 47N50)},
  MRNUMBER = {2194033 (2006k:81124)},
MRREVIEWER = {Jaouad Sahbani},
       DOI = {10.1063/1.2142837},
       URL = {http://dx.doi.org/10.1063/1.2142837},
}

@article {MR2227810,
    AUTHOR = {Rybkin, Alexei},
     TITLE = {The analytic structure of the reflection coefficient, a sum
              rule and a complete description of the {W}eyl {$m$}-function
              of half-line {S}chr\"odinger operators with {$L\sb 2$}-type
              potentials},
   JOURNAL = {Proc. Roy. Soc. Edinburgh Sect. A},
  FJOURNAL = {Proceedings of the Royal Society of Edinburgh. Section A.
              Mathematics},
    VOLUME = {136},
      YEAR = {2006},
    NUMBER = {3},
     PAGES = {615--632},
      ISSN = {0308-2105},
     CODEN = {PEAMDU},
   MRCLASS = {47E05 (34B20 34L25 34L40 81Q10)},
  MRNUMBER = {2227810 (2007a:47053)},
MRREVIEWER = {Dmitry G. Shepelsky},
       DOI = {10.1017/S0308210500005084},
       URL = {http://dx.doi.org/10.1017/S0308210500005084},
}

@incollection {MR2259114,
    AUTHOR = {Rybkin, Alexei},
     TITLE = {Preservation of the absolutely continuous spectrum: some
              extensions of a result by {M}olchanov-{N}ovitskii-{V}ainberg},
 BOOKTITLE = {Recent advances in differential equations and mathematical
              physics},
    SERIES = {Contemp. Math.},
    VOLUME = {412},
     PAGES = {271--281},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {2006},
   MRCLASS = {47E05 (34B20 34L20 34L25 81Q10)},
  MRNUMBER = {2259114 (2007g:47073)},
MRREVIEWER = {Alexander M. Gomilko},
}

@article {MR2432031,
    AUTHOR = {Rybkin, Alexei},
     TITLE = {On the evolution of a reflection coefficient under the
              {K}orteweg-de {V}ries flow},
   JOURNAL = {J. Math. Phys.},
  FJOURNAL = {Journal of Mathematical Physics},
    VOLUME = {49},
      YEAR = {2008},
    NUMBER = {7},
     PAGES = {072701, 15},
      ISSN = {0022-2488},
     CODEN = {JMAPAQ},
   MRCLASS = {35Q53 (34A55 34L25 35P25 35R30 37K15)},
  MRNUMBER = {2432031 (2009h:35382)},
       DOI = {10.1063/1.2951897},
       URL = {http://dx.doi.org/10.1063/1.2951897},
}

@article {MR2538578,
    AUTHOR = {Rybkin, Alexei and Vu Kim Tuan},
     TITLE = {A new interpolation formula for the {T}itchmarsh-{W}eyl
              {$m$}-function},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {137},
      YEAR = {2009},
    NUMBER = {12},
     PAGES = {4177--4185},
      ISSN = {0002-9939},
     CODEN = {PAMYAR},
   MRCLASS = {65D05 (34B20 34L40 41A05 47E05)},
  MRNUMBER = {2538578 (2010k:65023)},
MRREVIEWER = {Alexandru Ioan Mitrea},
       DOI = {10.1090/S0002-9939-09-09983-3},
       URL = {http://dx.doi.org/10.1090/S0002-9939-09-09983-3},
}

@article {MR2540891,
    AUTHOR = {Rybkin, Alexei},
     TITLE = {On the {M}archenko inverse scattering procedure with partial
              information on the potential},
   JOURNAL = {Inverse Problems},
  FJOURNAL = {Inverse Problems. An International Journal on the Theory and
              Practice of Inverse Problems, Inverse Methods and Computerized
              Inversion of Data},
    VOLUME = {25},
      YEAR = {2009},
    NUMBER = {9},
     PAGES = {095011, 34},
      ISSN = {0266-5611},
     CODEN = {INPEEY},
   MRCLASS = {35R30 (35P25 78A40)},
  MRNUMBER = {2540891 (2011a:35581)},
       DOI = {10.1088/0266-5611/25/9/095011},
       URL = {http://dx.doi.org/10.1088/0266-5611/25/9/095011},
}

@article {MR2558307,
    AUTHOR = {Rybkin, Alexei},
     TITLE = {On the boundary control approach to inverse spectral and
              scattering theory for {S}chr\"odinger operators},
   JOURNAL = {Inverse Probl. Imaging},
  FJOURNAL = {Inverse Problems and Imaging},
    VOLUME = {3},
      YEAR = {2009},
    NUMBER = {1},
     PAGES = {139--149},
      ISSN = {1930-8337},
   MRCLASS = {35L25 (34A55 35L05 49N45 93C20)},
  MRNUMBER = {2558307 (2011a:35313)},
MRREVIEWER = {Antonio C. G. Leit{\~a}o},
       DOI = {10.3934/ipi.2009.3.139},
       URL = {http://dx.doi.org/10.3934/ipi.2009.3.139},
}

@article {Ryb10,
    AUTHOR = {Rybkin, Alexei},
     TITLE = {Meromorphic solutions to the {K}d{V} equation with
              non-decaying initial data supported on a left half line},
   JOURNAL = {Nonlinearity},
  FJOURNAL = {Nonlinearity},
    VOLUME = {23},
      YEAR = {2010},
    NUMBER = {5},
     PAGES = {1143--1167},
      ISSN = {0951-7715},
     CODEN = {NONLE5},
   MRCLASS = {35Q53 (34A55 34L25 37K15)},
  MRNUMBER = {2630095 (2011i:35223)},
       DOI = {10.1088/0951-7715/23/5/007},
       URL = {http://dx.doi.org/10.1088/0951-7715/23/5/007},
}

@incollection {MR2683250,
    AUTHOR = {Rybkin, Alexei},
     TITLE = {Regularized perturbation determinants and {K}d{V} conservation
              laws for irregular initial profiles},
 BOOKTITLE = {Topics in operator theory. {V}olume 2. {S}ystems and
              mathematical physics},
    SERIES = {Oper. Theory Adv. Appl.},
    VOLUME = {203},
     PAGES = {427--444},
 PUBLISHER = {Birkh\"auser Verlag},
   ADDRESS = {Basel},
      YEAR = {2010},
   MRCLASS = {37K15 (34A55 34L40 35Q53 37K10)},
  MRNUMBER = {2683250},
}