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149 1844 y(1)34 b(ev)m(erywhere)k(and)c(realizes)g(a)g(unitary)g(equiv)
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1594 y Fo(1)955 1579 y Fq(\))993 1538 y Fo(2)1049 1579
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Fg(R)p Fe(+1)1651 2080 y Fj(\\)p Fo(\012)1772 1932 y
Fq(\()p Fm(r)p Fp( )t Fq(\)\()p Fm(r)p Fp(g)2166 1947
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2091 y Fg(R)p Fe(+1)2732 2080 y Fj(\\)p Fo(\012)2868
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%%Page: 9 9
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%%Page: 10 10
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%%Page: 20 20
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21 20 bop 458 185 a Fh(SOLUTIONS,)32 b(SPECTR)n(UM,)i(AND)e(D)n
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y Fm(hk)p Fp(P)1304 4123 y Fn(R)1357 4134 y Fg(T)1409
4108 y Fp( )t Fq(\()p Fp(t)p Fq(\))p Fm(k)1637 4067 y
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24 23 bop 149 168 a Fh(24)1213 b(A.)34 b(KISELEV)e(AND)g(Y.)h(LAST)149
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589 y(consider)33 b(the)g(follo)m(wing)d(mo)s(di\014ed)i(W)-8
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v Fp(n;)17 b(x)1370 821 y Fn(l)1396 806 y Fq(\))p Fp(a)1485
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(olev)149 1328 y(estimates)j(for)f(b)s(ounded)h(su\016cien)m(tly)h(smo)
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(higher)f(order)h(op)s(erators)f(and)h(systems.)42 b(In)24
b(particular,)149 1677 y(in)33 b(one)g(dimension,)e(a)i(self-adjoin)m
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Fp(n)g Fq(is)f(giv)m(en)h(b)m(y)149 1793 y(the)g(expression)584
1965 y(\()p Fp(Lf)11 b Fq(\)\()p Fp(x)p Fq(\))28 b(=)g(\()p
Fm(\000)p Fq(1\))1250 1924 y Fn(n)1297 1965 y Fq(\()p
Fp(p)1384 1980 y Fo(0)1423 1965 y Fp(f)1482 1924 y Fo(\()p
Fn(n)p Fo(\))1584 1965 y Fq(\))1622 1924 y Fo(\()p Fn(n)p
Fo(\))1746 1965 y Fq(+)22 b(\()p Fm(\000)p Fq(1\))2046
1924 y Fn(n)p Fj(\000)p Fo(1)2183 1965 y Fq(\()p Fp(p)2270
1980 y Fo(1)2309 1965 y Fp(f)2368 1924 y Fo(\()p Fn(n)p
Fj(\000)p Fo(1\))2560 1965 y Fq(\))2598 1924 y Fo(\()p
Fn(n)p Fj(\000)p Fo(1\))2812 1965 y Fq(+)g Fm(\001)17
b(\001)g(\001)k Fq(+)h Fp(p)3196 1980 y Fn(n)3242 1965
y Fp(f)149 2134 y Fq(and)36 b(a)f(set)h(of)e(self-adjoin)m(t)g(b)s
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i(in)m(tegration)d(b)m(y)i(parts:)543 2514 y Fp(W)635
2529 y Fn(L;x)747 2514 y Fq([)p Fp(f)5 b(;)17 b(g)t Fq(])27
b(=)1130 2390 y Fn(n)1080 2419 y Fk(X)1090 2629 y Fn(j)t
Fo(=1)1300 2386 y Fn(j)1244 2419 y Fk(X)1240 2629 y Fn(m)p
Fo(=1)1393 2514 y Fq(\()p Fm(\000)p Fq(1\))1595 2473
y Fn(m)1678 2433 y Fk(\000)1724 2514 y Fq(\()p Fp(p)1811
2529 y Fn(j)1847 2514 y Fp(f)1906 2473 y Fo(\()p Fn(j)t
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y Fo(\()p Fn(j)t Fj(\000)p Fn(m)p Fo(\))2895 2514 y Fq(\()p
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Fq(=)h Fp(\036;)1373 3069 y Fm(k)p Fp(u)p Fm(k)1529 3084
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y Fn(L)2239 3093 y Fe(2)2273 3084 y Fo(\()p Fn(B)2353
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3707 y(In)g(particular,)e(w)m(e)i(ha)m(v)m(e)149 3966
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25 24 bop 458 185 a Fh(SOLUTIONS,)32 b(SPECTR)n(UM,)i(AND)e(D)n
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2532 y Fq(the)g(op)s(erator)f(de\014ned)i(on)f(the)149
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2888 y Fm(\000)1669 2821 y Fp(d)1720 2785 y Fo(2)p 1641
2865 146 4 v 1641 2957 a Fp(dx)1747 2928 y Fo(2)1819
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4002 y Fj(\000)1478 3974 y Fe(1)p 1478 3986 V 1478 4028
a(4)1539 4043 y Fq(exp)q(\()p Fm(\006)p Fp(i)p Fq(\()1884
3975 y(2)p 1884 4020 49 4 v 1884 4111 a(3)1944 4043 y
Fp(x)2009 3974 y Fe(3)p 2009 3986 31 3 v 2009 4028 a(2)2076
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Fq(\()p Fp(x;)17 b(E)6 b Fq(\)\)\)\(1)22 b(+)g Fp(o)p
Fq(\(1\)\))149 4282 y Ff(as)35 b Fp(x)28 b Fm(!)f Fq(+)p
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4246 y Fj(0)1073 4306 y(\006)1132 4282 y Fq(\()p Fp(x;)17
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Fp(x)p Fq(\))1922 4245 y Fj(\000)1987 4218 y Fe(1)p 1987
4230 V 1987 4271 a(2)2032 4282 y Fp(:)249 4431 y Fq(Stark)30
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b(Indeed,)149 4677 y(for)32 b(a.e.)g(energy)h Fp(E)39
b Fq(here,)33 b(w)m(e)g(ha)m(v)m(e)g(a)f(solution)e Fp(u)p
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Fp(R)3006 4640 y Fj(\000)3071 4613 y Fe(1)p 3070 4625
V 3070 4666 a(2)3115 4677 y Fm(k)p Fp(u)p Fq(\()p Fp(x;)17
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eop
%%Page: 26 26
26 25 bop 149 168 a Fh(26)1213 b(A.)34 b(KISELEV)e(AND)g(Y.)h(LAST)149
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(1987)191 4342 y([7])41 b(M.)d(Christ)g(and)g(A.)g(Kiselev,)i
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b(J.M.)22 b(Com)n(b)r(es,)h Fi(Conne)l(ctions)i(b)l(etwe)l(en)f
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(time-evolution)320 4741 y(op)l(er)l(ators)p FB(,)d(In:)33
b(\\Di\013eren)n(tial)19 b(Equations)f(with)i(Applications)f(to)g
(Mathematical)g(Ph)n(ysics")f(\(W.F.)i(Ames,)320 4840
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b(Damanik,)g Fz(\013)p Fi(-c)l(ontinuity)i(pr)l(op)l(erties)h(of)f
(one-dimensional)i(quasicrystals,)g FB(Comm)n(un.)28
b(Math.)h(Ph)n(ys.)320 5039 y Fa(192)e FB(\(1998\),)f(169{182)p
eop
%%Page: 27 27
27 26 bop 458 185 a Fh(SOLUTIONS,)32 b(SPECTR)n(UM,)i(AND)e(D)n
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556 y([11])41 b(R.)31 b(del)g(Rio,)g(S.)g(Jitomirsk)-5
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b(L.C.)33 b(Ev)-5 b(ans,)34 b Fi(Partial)j(Di\013er)l(ential)e
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1353 y(Schr\177)-42 b(odinger)31 b(op)l(er)l(ators,)h
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FB(\(1989\),)g(213{229)149 1652 y([16])41 b(I.)36 b(Guarneri)f
Fi(Sp)l(e)l(ctr)l(al)i(pr)l(op)l(erties)h(of)g(quantum)e(di\013usion)i
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b(I.)24 b(Guarneri)f Fi(On)j(an)g(estimate)h(c)l(onc)l(erning)f
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Fa(21)f FB(\(1993\),)g(729{733)149 2051 y([18])41 b(S.)28
b(Jitomirsk)-5 b(a)n(y)n(a,)25 b(in)j(preparation)149
2150 y([19])41 b(S.)28 b(Jitomirsk)-5 b(a)n(y)n(a)25
b(and)i(Y.)h(Last,)f Fi(Dimensional)j(Hausdor\013)g(pr)l(op)l(erties)h
(of)g(singular)f(c)l(ontinuous)e(sp)l(e)l(ctr)l(a,)320
2250 y FB(Ph)n(ys.)f(Rev.)g(Lett.)h Fa(76)g FB(\(1996\),)e(1765{1769)
149 2350 y([20])41 b(S.)23 b(Jitomirsk)-5 b(a)n(y)n(a)20
b(and)i(Y.)g(Last,)h Fi(Power)j(law)g(sub)l(or)l(dinacy)g(and)f
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(ators,)320 2449 y FB(preprin)n(t)149 2549 y([21])41
b(S.)32 b(Jitomirsk)-5 b(a)n(y)n(a)29 b(and)j(Y.)g(Last,)h
Fi(Power)h(law)h(sub)l(or)l(dinacy)f(and)g(singular)g(sp)l(e)l(ctr)l
(a.)g FB(I)r(I.)f Fi(Line)h(op)l(er)l(ators.)320 2648
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Fi(Gr)l(owth)j(pr)l(op)l(erties)g(of)h(solutions)e(of)h(the)g(r)l(e)l
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3047 y(p)l(acket)p FB(,)d(Ph)n(ys.)d(Rev.)i(Lett.)g Fa(79)f
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3545 y([26])41 b(A.)c(Kiselev,)g(Y.)g(Last,)h(and)e(B.)g(Simon,)j
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4541 y([31])41 b(S.)29 b(Mizohata,)g Fi(The)j(The)l(ory)g(of)g(Partial)
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4940 y([33])41 b(M.)28 b(Reed)g(and)g(B.)g(Simon,)g Fi(Metho)l(ds)j(of)
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b(ork,)26 b(1978)p eop
%%Page: 28 28
28 27 bop 149 168 a Fh(28)1213 b(A.)34 b(KISELEV)e(AND)g(Y.)h(LAST)149
357 y FB([34])41 b(F.)31 b(Rellic)n(h,)746 336 y Fi(\177)731
357 y(Ub)l(er)h(das)i(asymptotische)g(V)-6 b(erhalten)33
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b FB(+)f Fz(\025u)28 b FB(=)g(0)k Fi(in)h(unend)t(lichen)320
462 y(Gebieten,)702 441 y FB(\177)692 462 y(Ub)r(er.)28
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149 562 y([35])41 b(C.)22 b(Remling,)h Fi(The)j(absolutely)f(c)l
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b(odinger)26 b(op)l(er)l(ators)f(with)320 662 y(de)l(c)l(aying)31
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b(Rogers,)e Fi(Hausdor\013)k(Me)l(asur)l(es,)h FB(Cam)n(bridge)26
b(Univ.)i(Press,)e(London,)h(1979)149 861 y([37])41 b(C.A.)29
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FB(Acta)d(Math.)g(Sto)r(c)n(k.)320 961 y Fa(109)f FB(\(1963\),)f
(207{240)149 1060 y([38])41 b(I.)28 b(Sc)n(h'nol,)f Fi(On)i(the)h(b)l
(ehavior)i(of)e(the)g(Schr\177)-42 b(odinger)32 b(e)l(quation,)e
FB(Math.)e(Sb.)g Fa(42)f FB(\(1957\),)f(273{286)149 1160
y([39])41 b(B.)28 b(Simon,)f Fi(Schr\177)-42 b(odinger)32
b(semigr)l(oups,)f FB(Bull.)d(Amer.)f(Math.)h(So)r(c.)f
Fa(7)p FB(\(1982\),)g(447{525)149 1259 y([40])41 b(B.)25
b(Simon,)h Fi(The)i(Neumann)e(L)l(aplacian)j(of)g(a)e(jel)t(ly)i(r)l
(ol)t(l,)g FB(Pro)r(c.)24 b(Amer.)h(Math.)g(So)r(c.)g
Fa(114)f FB(\(1992\))f(783{785)149 1359 y([41])41 b(B.)49
b(Simon,)54 b Fi(Bounde)l(d)d(eigenfunctions)f(and)g(absolutely)g(c)l
(ontinuous)f(sp)l(e)l(ctr)l(a)g(for)h(one-dimensional)320
1459 y(Schr\177)-42 b(odinger)31 b(op)l(er)l(ators,)h
FB(Pro)r(c.)26 b(Amer.)i(Math.)f(So)r(c.)h Fa(124)f FB(\(1996\),)f
(3361{3369)149 1558 y([42])41 b(G.)e(Stolz,)j Fi(Bounde)l(d)e
(solutions)h(and)f(absolute)h(c)l(ontinuity)e(of)i(Sturm-Liouvil)t(le)f
(op)l(er)l(ators,)k FB(J.)39 b(Math.)320 1658 y(Anal.)28
b(Appl.)g Fa(169)f FB(\(1992\),)f(210{228)149 1758 y([43])41
b(R.S.)28 b(Stric)n(hartz,)f Fi(F)-6 b(ourier)30 b(asymptotics)h(of)f
(fr)l(actal)h(me)l(asur)l(es,)f FB(J.)d(F)-7 b(unct.)29
b(Anal.)f Fa(89)f FB(\(1990\),)f(154{187)149 1857 y([44])41
b(N.)23 b(Vilenkin,)h Fi(Sp)l(e)l(cial)i(F)-6 b(unctions)24
b(and)h(the)g(The)l(ory)i(of)f(Gr)l(oup)f(R)l(epr)l(esentations,)h
FB(Nauk)-5 b(a,)23 b(Mosco)n(w,)f(1991)320 1957 y(\(in)28
b(Russian\))149 2227 y Fq(Departmen)m(t)33 b(of)f(Mathematics)149
2343 y(Univ)m(ersit)m(y)i(of)e(Chicago)149 2460 y(5734)g(S.)h(Univ)m
(ersit)m(y)g(Av)m(e.)149 2576 y(Chicago,)f(IL)h(60637)149
2692 y(email:)42 b(kiselev@math.uc)m(hicago.edu)149 2925
y(and)149 3157 y(Departmen)m(t)33 b(of)f(Mathematics)149
3273 y(California)e(Institute)j(of)f(T)-8 b(ec)m(hnology)149
3389 y(P)m(asadena,)34 b(CA)f(91125)149 3506 y(email:)42
b(ylast@cco.caltec)m(h.edu)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF