메뉴 건너뛰기




Volumn 25, Issue , 2006, Pages 409-430

Fourier-Bessel functions of singular continuous measures and their many asymptotics

Author keywords

Almost periodic Jacobi matrices; Fourier transform; Fourier Bessel functions; Generalized dimensions; Iterated function systems; Julia sets; Orthogonal polynomials; Potential theory; Quantum intermittency; Singular measures

Indexed keywords

ASYMPTOTIC STABILITY; FOURIER TRANSFORMS; ITERATIVE METHODS; PROBLEM SOLVING; QUANTUM THEORY; SET THEORY;

EID: 33846975759     PISSN: None     EISSN: 10689613     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (22)

References (44)
  • 1
    • 0031220833 scopus 로고    scopus 로고
    • Remarks on the relation between quantum dynamics and fractal spectra
    • J. M. BARBAROUX, J. M. COMBES, AND R. MONTCHO, Remarks on the relation between quantum dynamics and fractal spectra, J. Math. Anal. Appl., 213 (1997), pp. 698-772.
    • (1997) J. Math. Anal. Appl , vol.213 , pp. 698-772
    • BARBAROUX, J.M.1    COMBES, J.M.2    MONTCHO, R.3
  • 2
    • 0000938886 scopus 로고    scopus 로고
    • Fractal dimensions and the phenomenon of intermittency in quantum dynamics
    • J. M. BARBAROUX, F. GERMINET, AND S. TCHEREMCHANTSEV, Fractal dimensions and the phenomenon of intermittency in quantum dynamics, Duke Math. J., 110 (2001), pp. 161-193.
    • (2001) Duke Math. J , vol.110 , pp. 161-193
    • BARBAROUX, J.M.1    GERMINET, F.2    TCHEREMCHANTSEV, S.3
  • 3
    • 0035604405 scopus 로고    scopus 로고
    • Generalized fractal dimensions: Equivalence and basic properties
    • J. M. BARBAROUX, F. GERMINET, AND S. TCHEREMCHANTSEV, Generalized fractal dimensions: equivalence and basic properties, J. Math. Pures Appl., 80 (2001), pp. 977-1012.
    • (2001) J. Math. Pures Appl , vol.80 , pp. 977-1012
    • BARBAROUX, J.M.1    GERMINET, F.2    TCHEREMCHANTSEV, S.3
  • 4
    • 4644334752 scopus 로고    scopus 로고
    • Transfer matrices and transport for 1D Schrödinger operators with singular spectrum
    • J. M. BARBAROUX, F. GERMINET, AND S. TCHEREMCHANTSEV, Transfer matrices and transport for 1D Schrödinger operators with singular spectrum, Ann. Inst. Fourier, 54 (2004), pp. 787-830.
    • (2004) Ann. Inst. Fourier , vol.54 , pp. 787-830
    • BARBAROUX, J.M.1    GERMINET, F.2    TCHEREMCHANTSEV, S.3
  • 5
    • 0000587732 scopus 로고    scopus 로고
    • Anomalous transport in presence of singular continuous spectral measures
    • J. M. BARBAROUX AND H. SCHULZ-BALDES, Anomalous transport in presence of singular continuous spectral measures, Ann. Inst. H. Poincaré Phys. Théo., 71 (1999), pp. 539-559.
    • (1999) Ann. Inst. H. Poincaré Phys. Théo , vol.71 , pp. 539-559
    • BARBAROUX, J.M.1    SCHULZ-BALDES, H.2
  • 7
    • 0022421231 scopus 로고
    • Iterated function systems and the global construction of fractals
    • M. F. BARNSLEY AND S.G. DEMKO, Iterated function systems and the global construction of fractals, Proc. R. Soc. London, A 399 (1985), pp. 243-275.
    • (1985) Proc. R. Soc. London, A , vol.399 , pp. 243-275
    • BARNSLEY, M.F.1    DEMKO, S.G.2
  • 8
    • 84966204651 scopus 로고
    • Infinite-dimensional Jacobi matrices associated with Julia sets
    • M. F. BARNSLEY, J. S. GERONIMO, AND A. N. HARRINGTON, Infinite-dimensional Jacobi matrices associated with Julia sets, Proc. Am. Math. Soc., 88 (1983), pp. 625-630.
    • (1983) Proc. Am. Math. Soc , vol.88 , pp. 625-630
    • BARNSLEY, M.F.1    GERONIMO, J.S.2    HARRINGTON, A.N.3
  • 9
    • 35949019472 scopus 로고
    • Chaotic states of almost periodic Schrödinger operators
    • J. BELLISSARD, D. BESSIS, AND P. MOUSSA, Chaotic states of almost periodic Schrödinger operators, Phys. Rev. Lett., 49 (1982), pp. 702-704.
    • (1982) Phys. Rev. Lett , vol.49 , pp. 702-704
    • BELLISSARD, J.1    BESSIS, D.2    MOUSSA, P.3
  • 10
    • 0036628279 scopus 로고    scopus 로고
    • Phase-averaged transport for quasi-periodic Hamiltonians
    • J. BELLISSARD, I. GUARNERI, AND H. SCHULZ- BALDES, Phase-averaged transport for quasi-periodic Hamiltonians, Comm. Math. Phys., 227 (2002), pp. 515-539.
    • (2002) Comm. Math. Phys , vol.227 , pp. 515-539
    • BELLISSARD, J.1    GUARNERI, I.2    SCHULZ- BALDES, H.3
  • 11
    • 0041188298 scopus 로고
    • Orthogonal polynomials associated to almost periodic Schrödinger operators
    • D. BESSIS AND G. MANTICA, Orthogonal polynomials associated to almost periodic Schrödinger operators, J. Comp. Appl. Math., 48 (1993), pp. 17-32.
    • (1993) J. Comp. Appl. Math , vol.48 , pp. 17-32
    • BESSIS, D.1    MANTICA, G.2
  • 12
    • 85009367586 scopus 로고
    • Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms
    • Springer-Verlag, Berlinr
    • R. BOWEN, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Mathematics, 470, Springer-Verlag, Berlinr, 1975.
    • (1975) Lecture Notes in Mathematics , vol.470
    • BOWEN, R.1
  • 14
    • 0013464506 scopus 로고    scopus 로고
    • Fractal dimensions and quantum evolution associated with sparse potential Jacobi matrices
    • Long Time Behavior of Classical and Quantum Systems, World Sci. Publishing, River Edge, NJ
    • J. M. COMBES AND G. MANTICA, Fractal dimensions and quantum evolution associated with sparse potential Jacobi matrices, in Long Time Behavior of Classical and Quantum Systems, Ser. Concr. Appl. Math. 1, World Sci. Publishing, River Edge, NJ, 2001, pp. 107-123.
    • (2001) Ser. Concr. Appl. Math , vol.1 , pp. 107-123
    • COMBES, J.M.1    MANTICA, G.2
  • 15
    • 38248999656 scopus 로고
    • Asymptotics for the moments of singular distributions
    • W. GOH AND J. WIMP, Asymptotics for the moments of singular distributions, J. Approx. Theory, 74 (1993), pp. 301-334;
    • (1993) J. Approx. Theory , vol.74 , pp. 301-334
    • GOH, W.1    WIMP, J.2
  • 17
    • 0000167355 scopus 로고
    • Multifractal energy spectra and their dynamical implications
    • I. GUARNERI AND G. MANTICA, Multifractal energy spectra and their dynamical implications, Phys. Rev. Lett., 73 (1994), pp. 3379-3382.
    • (1994) Phys. Rev. Lett , vol.73 , pp. 3379-3382
    • GUARNERI, I.1    MANTICA, G.2
  • 18
    • 0003232182 scopus 로고    scopus 로고
    • I. GUARNERI AND H. SCHULZ-BALDES, Lower bounds on wave-packet propagation by packing dimensions of spectral measures, Math. Phys. Elec. J., 5 (1999), pap. 1.
    • I. GUARNERI AND H. SCHULZ-BALDES, Lower bounds on wave-packet propagation by packing dimensions of spectral measures, Math. Phys. Elec. J., 5 (1999), pap. 1.
  • 19
    • 0000881439 scopus 로고    scopus 로고
    • Intermittent lower bound on quantum diffusion
    • I. GUARNERI AND H. SCHULZ-BALDES, Intermittent lower bound on quantum diffusion, Lett. Math. Phys., 49 (1999), pp. 317-324.
    • (1999) Lett. Math. Phys , vol.49 , pp. 317-324
    • GUARNERI, I.1    SCHULZ-BALDES, H.2
  • 20
    • 0033276142 scopus 로고    scopus 로고
    • Upper bounds for quantum dynamics governed by Jacobi matrices with self-similar spectra
    • I. GUARNERI AND H. SCHULZ-BALDES, Upper bounds for quantum dynamics governed by Jacobi matrices with self-similar spectra, Rev. Math. Phys., 11 (1999), pp. 1249-1268.
    • (1999) Rev. Math. Phys , vol.11 , pp. 1249-1268
    • GUARNERI, I.1    SCHULZ-BALDES, H.2
  • 21
    • 0010843256 scopus 로고
    • Inverse problems in fractal construction: Moment method solution
    • C. R. HANDY AND G. MANTICA, Inverse problems in fractal construction: moment method solution, Physica D, 43 (1990), pp. 17-36.
    • (1990) Physica D , vol.43 , pp. 17-36
    • HANDY, C.R.1    MANTICA, G.2
  • 22
    • 0001265433 scopus 로고
    • Fractals and self-similarity
    • J. HUTCHINSON, Fractals and self-similarity, Indiana J. Math., 30 (1981), pp. 713-747.
    • (1981) Indiana J. Math , vol.30 , pp. 713-747
    • HUTCHINSON, J.1
  • 24
    • 0000443928 scopus 로고    scopus 로고
    • What determines the spreading of a wave packet?
    • R. KETZMERICK, K. KRUSE, S. KRAUT, AND T. GEISEL, What determines the spreading of a wave packet?, Phys. Rev. Lett., 79 (1997), pp. 1959-1963.
    • (1997) Phys. Rev. Lett , vol.79 , pp. 1959-1963
    • KETZMERICK, R.1    KRUSE, K.2    KRAUT, S.3    GEISEL, T.4
  • 25
    • 4244105543 scopus 로고
    • Slow decay of temporal correlations in quantum systems with Cantor spectra
    • R. KETZMERICK, G. PETSCHEL, AND T. GEISEL, Slow decay of temporal correlations in quantum systems with Cantor spectra, Phys. Rev. Lett., 69 (1992), pp. 695-698.
    • (1992) Phys. Rev. Lett , vol.69 , pp. 695-698
    • KETZMERICK, R.1    PETSCHEL, G.2    GEISEL, T.3
  • 26
    • 0141541804 scopus 로고    scopus 로고
    • Dynamical upper bounds on wavepaket spreading
    • R. KILLIP, A. KISELEV, AND Y. LAST, Dynamical upper bounds on wavepaket spreading, Amer. J. Math., 125 (2003), pp. 1165-1198.
    • (2003) Amer. J. Math , vol.125 , pp. 1165-1198
    • KILLIP, R.1    KISELEV, A.2    LAST, Y.3
  • 27
    • 0034652879 scopus 로고    scopus 로고
    • Solutions, spectrum, and dynamics for Schrödinger operators on infinite domains
    • A. KISELEV AND Y. LAST, Solutions, spectrum, and dynamics for Schrödinger operators on infinite domains, Duke Math. J., 102 (2000), pp. 125-150.
    • (2000) Duke Math. J , vol.102 , pp. 125-150
    • KISELEV, A.1    LAST, Y.2
  • 28
    • 0002706785 scopus 로고
    • Mean quadratic variations and Fourier asymptotic of self-similar measures
    • K. S. LAU AND J. WANG, Mean quadratic variations and Fourier asymptotic of self-similar measures, Monatsh. Math., 115 (1993), pp. 99-132.
    • (1993) Monatsh. Math , vol.115 , pp. 99-132
    • LAU, K.S.1    WANG, J.2
  • 29
    • 11644280613 scopus 로고
    • Asymptotic expansions for Fourier transform of singular self-affine measures
    • K. A. MAKAROV, Asymptotic expansions for Fourier transform of singular self-affine measures, J. Math. Anal. and Appl., 186 (1994), pp. 259-286.
    • (1994) J. Math. Anal. and Appl , vol.186 , pp. 259-286
    • MAKAROV, K.A.1
  • 30
    • 0030509545 scopus 로고    scopus 로고
    • A Stieltjes technique for computing Jacobi matrices associated with singular measures
    • G. MANTICA, A Stieltjes technique for computing Jacobi matrices associated with singular measures, Constr. Appr., 12 (1996), pp. 509-530.
    • (1996) Constr. Appr , vol.12 , pp. 509-530
    • MANTICA, G.1
  • 31
    • 0031118853 scopus 로고    scopus 로고
    • Quantum intermittency in almost periodic systems derived from their spectral properties
    • G. MANTIC A, Quantum intermittency in almost periodic systems derived from their spectral properties, Physica D, 103 (1997), pp. 576-589.
    • (1997) Physica D , vol.103 , pp. 576-589
    • MANTIC A, G.1
  • 32
    • 0000306155 scopus 로고    scopus 로고
    • Wave propagation in almost-periodic structures
    • G. MANTICA, Wave propagation in almost-periodic structures, Physica D, 109 (1997), pp. 113-127.
    • (1997) Physica D , vol.109 , pp. 113-127
    • MANTICA, G.1
  • 33
    • 11644297481 scopus 로고    scopus 로고
    • G. MANTICA, Quantum intermittency: old or new phenomenon?, J. Phys. IV France, 8 (1998), pp. Pr6-253-262.
    • G. MANTICA, Quantum intermittency: old or new phenomenon?, J. Phys. IV France, 8 (1998), pp. Pr6-253-262.
  • 34
    • 33847005497 scopus 로고    scopus 로고
    • Fourier transforms of orthogonal polynomials of singular continuous spectral measures, in Applications and Computation of Orthogonal Polynomials, Internat
    • W. Gautschi, G. H. Golub, and G. Opfer, eds, Birkhäuser, Basel
    • G. MANTICA Fourier transforms of orthogonal polynomials of singular continuous spectral measures, in Applications and Computation of Orthogonal Polynomials, Internat. Ser. Numer. Math., Vol. 131, W. Gautschi, G. H. Golub, and G. Opfer, eds., Birkhäuser, Basel, 1999, pp. 153-163.
    • (1999) Ser. Numer. Math , vol.131 , pp. 153-163
    • MANTICA, G.1
  • 35
    • 0034159016 scopus 로고    scopus 로고
    • On computing Jacobi matrices associated with recurrent and Möbius iterated functions systems
    • G. MANTICA On computing Jacobi matrices associated with recurrent and Möbius iterated functions systems, J. Comp. Appl. Math., 115 (2000), pp. 419-431.
    • (2000) J. Comp. Appl. Math , vol.115 , pp. 419-431
    • MANTICA, G.1
  • 36
    • 33846985347 scopus 로고    scopus 로고
    • G. MANTICA AND S. VAIENTI, The asymptotic behaviour of the Fourier transforms of orthogonal polynomials I: mellin transform techniques, preprint mp-arc 04-314, 2004, to appear in Annales Henri Poincaré.
    • G. MANTICA AND S. VAIENTI, The asymptotic behaviour of the Fourier transforms of orthogonal polynomials I: mellin transform techniques, preprint mp-arc 04-314, 2004, to appear in Annales Henri Poincaré.
  • 37
    • 33846991688 scopus 로고    scopus 로고
    • G. MANTICA AND D. GUZZETTI, The asymptotic behaviour of the Fourier transforms of orthogonal polynomials II: IFS measures and quantum mechanics, preprint mp-arc 04-361, 2004, to appear in Annales Henri Poincaré.
    • G. MANTICA AND D. GUZZETTI, The asymptotic behaviour of the Fourier transforms of orthogonal polynomials II: IFS measures and quantum mechanics, preprint mp-arc 04-361, 2004, to appear in Annales Henri Poincaré.
  • 39
    • 4243811611 scopus 로고    scopus 로고
    • Anomalous diffusion properties of wave packets on quasiperiodic chains
    • F. PIÉCHON Anomalous diffusion properties of wave packets on quasiperiodic chains, Phys. Rev. Lett., 76 (1996), pp. 4372-4375.
    • (1996) Phys. Rev. Lett , vol.76 , pp. 4372-4375
    • PIÉCHON, F.1
  • 41
    • 0001319988 scopus 로고
    • Fourier asymptotics of fractal measures
    • R. S. STRICHARTZ, Fourier asymptotics of fractal measures, J. Funct. Anal., 89 (1990), pp. 154-187.
    • (1990) J. Funct. Anal , vol.89 , pp. 154-187
    • STRICHARTZ, R.S.1
  • 42
    • 0001482864 scopus 로고
    • Self-similar measures and their Fourier transforms I
    • R. S. STRICHARTZ, Self-similar measures and their Fourier transforms I, Indiana U. Math. J., 39 (1990), pp. 797-817.
    • (1990) Indiana U. Math. J , vol.39 , pp. 797-817
    • STRICHARTZ, R.S.1
  • 43
    • 84968466245 scopus 로고
    • Self-similar measures and their Fourier transforms II
    • R. S. STRICHARTZ, Self-similar measures and their Fourier transforms II, Trans. Amer. Math. Soc., 336 (1993), pp. 335-361.
    • (1993) Trans. Amer. Math. Soc , vol.336 , pp. 335-361
    • STRICHARTZ, R.S.1
  • 44
    • 0037428622 scopus 로고    scopus 로고
    • Mixed lower bounds for quantum transport
    • S. TCHEREMCHANTSEV, Mixed lower bounds for quantum transport, J. Funct. Anal. 107 (2003), pp. 247-282.
    • (2003) J. Funct. Anal , vol.107 , pp. 247-282
    • TCHEREMCHANTSEV, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.