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Volumn 200, Issue , 1999, Pages 77-117

Harmonic analysis of fractal processes via C*-algebras

Author keywords

C* algebras; Endomorphisms; Fractals; Hilbert space; Inner functions; Wavelet

Indexed keywords


EID: 0002931954     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/mana.19992000105     Document Type: Article
Times cited : (6)

References (50)
  • 1
    • 0001069474 scopus 로고
    • Gibbs states of a one-dimensional quantum lattice
    • ARAKI, H.: Gibbs States of a One-Dimensional Quantum Lattice, Comm. Math. Phys. 14 (1969), 120-157
    • (1969) Comm. Math. Phys. , vol.14 , pp. 120-157
    • Araki, H.1
  • 2
    • 0003205924 scopus 로고
    • Continuous analogues of fock space
    • ARVESON, W. B.: Continuous Analogues of Fock Space, Mem. Amer. Math. Soc. 80 (1989)
    • (1989) Mem. Amer. Math. Soc. , vol.80
    • Arveson, W.B.1
  • 6
    • 0002989240 scopus 로고    scopus 로고
    • Endomorphisms of B(H), quantization, nonlinear partial differential equations, and operator algebra
    • Cambridge, Massachusetts, 1994 (W. ARVESON, T. BRANSON, and I. SEGAL, eds.), Amer. Math. Soc., Providence
    • BRATTELI, O., JORGENSEN, P. E. T., and PRICE, G. L.: Endomorphisms of B(H), Quantization, Nonlinear Partial Differential Equations, and Operator Algebra (Cambridge, Massachusetts, 1994) (W. ARVESON, T. BRANSON, and I. SEGAL, eds.), Proc. Sympos. Pure Math., Vol. 59, pp. 93-138, Amer. Math. Soc., Providence, 1996
    • (1996) Proc. Sympos. Pure Math. , vol.59 , pp. 93-138
    • Bratteli, O.1    Jorgensen, P.E.T.2    Price, G.L.3
  • 10
    • 84983630509 scopus 로고
    • Ondelettes, analyses multirésolutions et filtres miroir en quadrature
    • COHEN, A.: Ondelettes, Analyses Multirésolutions et Filtres Miroir en Quadrature, Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (1990), 439-459
    • (1990) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.7 , pp. 439-459
    • Cohen, A.1
  • 12
    • 3042722951 scopus 로고
    • Simple C*-algebras generated by isometries
    • CUNTZ, J.: Simple C*-Algebras Generated by Isometries, Comm. Math. Phys. 57 (1977), 173-185
    • (1977) Comm. Math. Phys. , vol.57 , pp. 173-185
    • Cuntz, J.1
  • 18
    • 34250967631 scopus 로고
    • Zur theorie der orthogonalen funktionen-systeme
    • HAAR, A.: Zur Theorie der orthogonalen Funktionen-Systeme, Math. Ann. 69 (1910), 331-371
    • (1910) Math. Ann. , vol.69 , pp. 331-371
    • Haar, A.1
  • 19
    • 0024903928 scopus 로고
    • Continuous and discrete wavelet transforms
    • HEIL, C., and WALNUT, D.: Continuous and Discrete Wavelet Transforms, SIAM Rev. 31 (1989), 628-666
    • (1989) SIAM Rev. , vol.31 , pp. 628-666
    • Heil, C.1    Walnut, D.2
  • 21
    • 0001265433 scopus 로고
    • Fractals and self-similarity
    • HUTCHINSON, J. E.: Fractals and Self-Similarity, Indiana Univ. Math. J. 30 (1981), 713-747
    • (1981) Indiana Univ. Math. J. , vol.30 , pp. 713-747
    • Hutchinson, J.E.1
  • 22
    • 38149146849 scopus 로고
    • On a family of almost commuting endomorphisms
    • JONES, V. F. R.: On a Family of Almost Commuting Endomorphisms, J. Funct. Anal. 122 (1994), 84-90
    • (1994) J. Funct. Anal. , vol.122 , pp. 84-90
    • Jones, V.F.R.1
  • 23
    • 0039648123 scopus 로고    scopus 로고
    • A duality for endomorphisms of Von Neumann algebras
    • JORGENSEN, P. E. T.: A Duality for Endomorphisms of von Neumann Algebras, J. Math. Phys. 37 (1996), 1521-1538
    • (1996) J. Math. Phys. , vol.37 , pp. 1521-1538
    • Jorgensen, P.E.T.1
  • 25
    • 0002590373 scopus 로고
    • Harmonic analysis and fractal limit-measures induced by representations of a certain C*-algebra
    • JORGENSEN, P. E. T., and PEDERSEN, S.: Harmonic Analysis and Fractal Limit-Measures Induced by Representations of a Certain C*-Algebra, J. Funct. Anal. 125 (1994), 90-110
    • (1994) J. Funct. Anal. , vol.125 , pp. 90-110
    • Jorgensen, P.E.T.1    Pedersen, S.2
  • 26
    • 0003132998 scopus 로고    scopus 로고
    • Harmonic analysis of fractal measures
    • JORGENSEN, P. E. T., and PEDERSEN, S.: Harmonic Analysis of Fractal Measures, Constr. Approx. 12 (1996), 1-30
    • (1996) Constr. Approx. , vol.12 , pp. 1-30
    • Jorgensen, P.E.T.1    Pedersen, S.2
  • 27
    • 0011041049 scopus 로고
    • Estimates on the spectrum of fractals arising from affine iterations, fractal geometry and stochastics
    • Finsterbergen, C. BANDT, S. GRAF, and M. ZÄHLE, eds., Birkhäuser Basel
    • JORGENSEN, P. E. T., and PEDERSEN, S.: Estimates on the Spectrum of Fractals Arising from Affine Iterations, Fractal Geometry and Stochastics (Finsterbergen, 1994) (C. BANDT, S. GRAF, and M. ZÄHLE, eds.), Progress in Probability, Vol. 37, pp. 191-219, Birkhäuser Basel, 1995
    • (1994) Progress in Probability , vol.37 , pp. 191-219
    • Jorgensen, P.E.T.1    Pedersen, S.2
  • 28
    • 84967782961 scopus 로고
    • Harmonic analysis of fractal measures induced by representations of a certain C*-algebra
    • JORGENSEN, P. E. T., and PEDERSEN, S.: Harmonic Analysis of Fractal Measures Induced by Representations of a Certain C*-Algebra, Bull. Amer. Math. Soc. (N.S.) 29 (1993), 228-234
    • (1993) Bull. Amer. Math. Soc. (N.S.) , vol.29 , pp. 228-234
    • Jorgensen, P.E.T.1    Pedersen, S.2
  • 29
    • 21844521167 scopus 로고
    • Coherent states on the q-canonical commutation relations
    • JORGENSEN, P. E. T., and WERNER, R. F.: Coherent States on the q-Canonical Commutation Relations, Comm. Math. Phys. 164 (1994), 455-471
    • (1994) Comm. Math. Phys. , vol.164 , pp. 455-471
    • Jorgensen, P.E.T.1    Werner, R.F.2
  • 30
    • 0001013148 scopus 로고
    • Endomorphisms of B (H) and Cuntz algebras
    • LACA, M.: Endomorphisms of B (H) and Cuntz Algebras, J. Operator Theory 30 (1993), 85-108
    • (1993) J. Operator Theory , vol.30 , pp. 85-108
    • Laca, M.1
  • 31
    • 0040799572 scopus 로고    scopus 로고
    • Tiling the line with translates of one tile
    • LAGARIAS, J. C., and WANG, Y.: Tiling the Line with Translates of one Tile, Invent. Math. 124 (1996), 341-365
    • (1996) Invent. Math. , vol.124 , pp. 341-365
    • Lagarias, J.C.1    Wang, Y.2
  • 33
    • 0000382625 scopus 로고
    • Fonction zêta de Riemann et conjecture de Weyl-Berry pour les tambours fractals
    • LAPIDUS, M. L., AND POMERANCE, C.: Fonction Zêta de Riemann et Conjecture de Weyl-Berry pour les Tambours Fractals, C. R. Acad. Sci. Paris Sér. I Math. 310 (1990), 343-348
    • (1990) C. R. Acad. Sci. Paris Sér. I Math. , vol.310 , pp. 343-348
    • Lapidus, M.L.1    Pomerance, C.2
  • 34
    • 34250512548 scopus 로고
    • Unitary representations of group extensions, I
    • MACKEY, G. W.: Unitary Representations of Group Extensions, I, Acta Math. 99 (1958), 265-311
    • (1958) Acta Math. , vol.99 , pp. 265-311
    • Mackey, G.W.1
  • 36
    • 0003322586 scopus 로고
    • The Ruelle-Araki transfer operator in classical statistical mechanics
    • Springer-Verlag, Berlin
    • MAYER, D. H.: The Ruelle-Araki Transfer Operator in Classical Statistical Mechanics, Lecture Notes in Phys. 123, Springer-Verlag, Berlin, 1980
    • (1980) Lecture Notes in Phys. , vol.123
    • Mayer, D.H.1
  • 37
    • 0003544046 scopus 로고
    • SIAM, Philadelphia, (translated from the French and with a foreword by ROBERT D. RYAN).
    • MEYER, Y.: Wavelets: Algorithms & Applications, SIAM, Philadelphia, 1993 (translated from the French and with a foreword by ROBERT D. RYAN).
    • (1993) Wavelets: Algorithms & Applications
    • Meyer, Y.1
  • 38
    • 0004198869 scopus 로고
    • Cambridge University Press, Cambridge, translation of 1990 French original Ondelettes et Opérateurs, Hermann, Paris, 1990
    • MEYER, Y.: Wavelets and Operators, Cambridge University Press, Cambridge, 1992 (translation of 1990 French original Ondelettes et Opérateurs, Hermann, Paris, 1990)
    • (1992) Wavelets and Operators
    • Meyer, Y.1
  • 41
    • 0012991978 scopus 로고
    • Induced representations and a new proof of the imprimitivity theorem
    • ØRSTED, B.: Induced Representations and a New Proof of the Imprimitivity Theorem, J. Funct. Anal. 31 (1979), 355-359
    • (1979) J. Funct. Anal. , vol.31 , pp. 355-359
    • ØRsted, B.1
  • 46
    • 0004179588 scopus 로고
    • Dynamical zeta functions for piecewise monotone maps of the interval
    • RUELLE, D.: Dynamical Zeta Functions for Piecewise Monotone Maps of the Interval, Amer. Math. Soc., CRM Monograph Series 4 (1994)
    • (1994) Amer. Math. Soc., CRM Monograph Series 4
    • Ruelle, D.1
  • 49
    • 0001418208 scopus 로고
    • Construction of Markov partitionings
    • SINAI, YA.: Construction of Markov Partitionings, Functional Anal. Appl. 2 (1968), 245-253
    • (1968) Functional Anal. Appl. , vol.2 , pp. 245-253
    • Sinai, Y.A.1
  • 50
    • 0001319988 scopus 로고
    • Fourier asymptotics of fractal measures
    • STRICHARTZ, R. S.: Fourier Asymptotics of Fractal Measures, J. Funct. Anal. 89 (1990), 154-187
    • (1990) J. Funct. Anal. , vol.89 , pp. 154-187
    • Strichartz, R.S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.