\ifx\undefined\bysame \newcommand{\bysame}{\leavevmode\hbox to3em{\hrulefill}\,} \fi \begin{thebibliography}{BrJo96b} \bibitem[Ada62]{Ada62} J.F. Adams, {\em Vector fields on spheres}, Ann. of Math. (2) {\bf 75} (1962), 603--632. \bibitem[BaRu96]{BaRu96} V.~Baladi and D.~Ruelle, {\em Sharp determinants}, Invent. Math. {\bf 123} (1996), 553--574. \bibitem[BJP96]{BJP96} Ola Bratteli, Palle~E.T. Jorgensen, and Geoffrey~L. Price, {\em Endomorphisms of $\mathcal{B}(\mathcal{H})$}, Quantization, nonlinear partial differential equations, and operator algebra (William Arveson, Thomas Branson, and Irving Segal, eds.), Proc. Sympos. Pure Math., vol.~59, American Mathematical Society, 1996, pp.~93--138. \bibitem[BrJo96a]{BrJo96a} Ola Bratteli and Palle~E.T. Jorgensen, {\em Endomorphisms of $\mathcal{B}(\mathcal{H})$, {II}: {F}initely correlated states on $\mathcal{O}_n$}, J.~Funct.\ Anal., to appear. \bibitem[BrJo96b]{BrJo96b} Ola Bratteli and Palle~E.T. Jorgensen, {\em Iterated function systems and permutation representations of the {C}untz algebra}, submitted to Mem.\ Amer.\ Math.\ Soc., 1996. \bibitem[Bro65]{Bro65} Hans Brolin, {\em Invariant sets under iteration of rational functions.}, Ark. Mat. {\bf 6} (1965), 103--144. \bibitem[BrRoII]{BrRoII} Ola Bratteli and Derek~W. Robinson, {\em Operator algebras and quantum statistical mechanics, vol.\ {II}}, 2nd ed., Springer-Verlag, Berlin--New York, 1996. \bibitem[CaGa93]{CaGa93} Lennart Carleson and Theodore~W. Gamelin, {\em Complex dynamics}, Springer-Verlag, New York, 1993. \bibitem[CFS82]{CFS82} I.P. Cornfeld, S.V. Fomin, and Ya.~G. Sinai, {\em Ergodic theory}, Grundlehren der mathematischen {W}issenschaften, vol. 245, Springer-Verlag, New York, 1982, translated from the Russian by A.B. Sosinskii. \bibitem[CoDa96]{CoDa96} Albert Cohen and Ingrid Daubechies, {\em A new technique to estimate the regularity of refinable functions}, Rev. Mat. Iberoamericana {\bf 12} (1996), 527--591. \bibitem[Coh90]{Coh90} A.~Cohen, {\em Ondelettes, analyses multir\'{e}solutions et filtres miroirs en quadrature}, Ann. Inst. H. Poincar\'{e} Anal. Non Lineaire {\bf 7} (1990), 439--459. \bibitem[CoMa95]{CoMa95} Carl~C. Cowen and Barbara~D. MacCluer, {\em Composition operators on spaces of analytic functions}, CRC Press, Boca Raton, FL, 1995. \bibitem[CoRy95]{CoRy95} Albert Cohen and Robert~D. Ryan, {\em Wavelets and multiscale signal processing}, Applied Mathematics and Mathematical Computation, vol.~11, Chapman \& Hall, London, 1995, translated from the French by Ryan; revised version of Cohen's doctoral thesis {\itshape Ondelettes et traitement num\'{e}rique du signal,} Masson, Paris, 1992. \bibitem[Cun77]{Cun77} Joachim Cuntz, {\em Simple ${C}^*$-al\-ge\-bras generated by isometries}, Comm. Math. Phys. {\bf 57} (1977), 173--185. \bibitem[DaPi96]{DaPi96} Ken~R. Davidson and David~R. Pitts, {\em Free semigroup algebras}, preprint, University of Waterloo, 1996. \bibitem[Dau92]{Dau92} Ingrid Daubechies, {\em Ten lectures on wavelets}, CBMS-NSF Regional Conf. Ser. in Appl. Math., vol.~61, Society for Industrial and Applied Mathematics, Philadelphia, 1992. \bibitem[GrHa94]{GrHa94} Karlheinz Gr\"ochenig and Andrew Haas, {\em Self-similar lattice tilings}, J.~Fourier Anal. Appl. {\bf 1} (1994), 131--170. \bibitem[GrMa92]{GrMa92} Karlheinz Gr\"ochenig and W.R. Madych, {\em Multiresolution analysis, {H}aar bases, and self-similar tilings of $\mathbf{R}^n$}, IEEE Trans. Inform. Theory {\bf 38} (1992), 556--568. \bibitem[Ho96]{Ho96} Mark~C. Ho, {\em Properties of slant {T}oeplitz operators}, preprint, Purdue University, 1996. \bibitem[HoJa96]{HoJa96} William~E. Hornor and James~E. Jamison, {\em Weighted composition operators on {H}ilbert spaces of vector-valued functions}, Proc. Amer. Math. Soc. {\bf 124} (1996), 3123--3130. \bibitem[Hut81]{Hut81} John~E. Hutchinson, {\em Fractals and self-similarity}, Indiana Univ. Math. J. {\bf 30} (1981), 713--747. \bibitem[JoPe94]{JoPe94} Palle~E.T. Jorgensen and Steen Pedersen, {\em Harmonic analysis and fractal limit-measures induced by representations of a certain ${C}^*$-al\-ge\-bra}, J. Funct. Anal. {\bf 125} (1994), 90--110. \bibitem[JoPe96]{JoPe96} Palle~E.T. Jorgensen and Steen Pedersen, {\em Harmonic analysis of fractal measures}, Constr. Approx. {\bf 12} (1996), 1--30. \bibitem[Jor95]{Jor95} Palle~E.T. Jorgensen, {\em Harmonic analysis of fractal processes via ${C}^*$-al\-ge\-bras}, preprint, The University of Iowa, 1995. \bibitem[Kea72]{Kea72} Michael Keane, {\em Strongly mixing $g$-measures}, Invent. Math. {\bf 16} (1972), 309--324. \bibitem[Lam86]{Lam86} Alan Lambert, {\em Hyponormal composition operators}, Bull. London Math. Soc. {\bf 18} (1986), 395--400. \bibitem[LaPh89]{LaPh89} Peter~D. Lax and Ralph~S. Phillips, {\em Scattering theory}, 2nd ed., Pure and Applied Mathematics, vol.~26, Academic Press, Inc., Boston, 1989, with appendices by Cathleen S. Morawetz and Georg Schmidt. \bibitem[LaSt91]{LaSt91} Yu.~D. Latushkin and A.~M. St\"epin, {\em Weighted shift operators and linear extensions of dynamical systems}, Russian Math. Surveys {\bf 46} (1991), 95--165, translation of {\itshape Akademiya Nauk SSSR i Moskovskoe Matematicheskoe Obshchestvo, Uspekhi Matematicheskikh Nauk} {\bfseries 46} (1991), 85--143, 240. \bibitem[Mal89]{Mal89} Stephane~G. Mallat, {\em Multiresolution approximations and wavelet orthonormal bases of ${L}^{2}(\mathbf{R})$}, Trans. Amer. Math. Soc. {\bf 315} (1989), 69--87. \bibitem[MePa93]{MePa93} Yves Meyer and Freddy Paiva, {\em Remarques sur la construction des ondelettes orthogonales}, J. Anal. Math. {\bf 60} (1993), 227--240. \bibitem[Mey87]{Mey87} Yves Meyer, {\em Ondelettes, fonctions splines et analyses gradu\'ees}, Rend. Sem. Mat. Univ. Politec. Torino {\bf 45} (1987), 1--42. \bibitem[Mey92b]{Mey92b} Yves Meyer, {\em Ondelettes et algorithmes concurrents}, Actualit\'{e} Scientifiques et Industrielles, vol. 1435, Hermann, Paris, 1992. \bibitem[Mey93]{Mey93} Yves Meyer, {\em Wavelets: {A}lgorithms \& applications}, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 1993, translated from the French and with a foreword by Robert D. Ryan. \bibitem[MRF96]{MRF96} Peter~R. Massopust, David~K. Ruch, and Patrick~J. Van~Fleet, {\em On the support properties of scaling vectors}, Appl. Comput. Harmon. Anal. {\bf 3} (1996), 229--238. \bibitem[PaPo90]{PaPo90} William Parry and Mark Pollicott, {\em Zeta functions and the periodic orbit structure of hyperbolic dynamics}, Ast\'erisque, vol. 187--188, Soci\'et\'e Math\'ematique de France, Paris, 1990. \bibitem[Pow88]{Pow88} Robert~T. Powers, {\em An index theory for semigroups of ${}^*$-en\-do\-mor\-phisms of $\mathcal{B}(\mathcal{H})$ and type $\mathrm{II}_1$ factors}, Canad. J. Math. {\bf 40} (1988), 86--114. \bibitem[Rue94]{Rue94} D.~Ruelle, {\em Dynamical zeta functions for piecewise monotone maps of the interval}, CRM Monograph Series, vol.~4, American Mathematical Society, Providence, 1994. \bibitem[SzFo70]{SzFo70} B\'{e}la Sz\H{o}kefalvi-Nagy and Ciprian Foias, {\em Harmonic analysis of operators on {H}ilbert space}, North-Holland, Amsterdam--London, Elsevier, New York, Akad\'{e}miai Kiad\'{o}, Budapest, 1970, translation and revised edition of the original French edition, Masson et Cie, Paris, Akad\'{e}miai Kiad\'{o}, Budapest, 1967. \bibitem[Wal82]{Wal82} Peter Walters, {\em An introduction to ergodic theory}, Graduate Texts in Mathematics, vol.~79, Springer-Verlag, New York, 1982. \bibitem[Wal96]{Wal96} Peter Walters, {\em Topological {W}iener-{W}intner ergodic theorems and a random ${L}^{2}$ ergodic theorem}, Ergodic Theory Dynam. Systems {\bf 16} (1996), 179--206. \end{thebibliography}