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Volumn 200, Issue 1, 2003, Pages 118-149

Polynomials of Meixner's type in infinite dimensions - Jacobi fields and orthogonality measures

Author keywords

Gamma measure; L vy process; Meixner measure; Meixner's polynomials; Pascal measure

Indexed keywords


EID: 0038286466     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-1236(02)00081-2     Document Type: Article
Times cited : (38)

References (30)
  • 2
    • 0003712691 scopus 로고
    • Expansions in Eigenfunctions of Selfadjoint Operators
    • American Mathematical Society, Providence, RI
    • Yu.M. Berezansky, Expansions in Eigenfunctions of Selfadjoint Operators, American Mathematical Society, Providence, RI, 1968.
    • (1968)
    • Berezansky, Yu.M.1
  • 3
    • 0037953756 scopus 로고    scopus 로고
    • On the theory of commutative Jacobi fields
    • Yu.M. Berezansky, On the theory of commutative Jacobi fields, Methods Funct. Anal. Topology 4 (1) (1998) 1-31.
    • (1998) Methods Funct. Anal. Topology , vol.4 , Issue.1 , pp. 1-31
    • Berezansky, Yu.M.1
  • 4
    • 0038630107 scopus 로고    scopus 로고
    • Infinite-dimensional non-Gaussian analysis connected with generalized translation operators
    • H. Heyer, J. Marion (Eds.), World Scientific, Singapore
    • Yu.M. Berezansky, Infinite-dimensional non-Gaussian analysis connected with generalized translation operators, in: H. Heyer, J. Marion (Eds.), Analysis on Infinite-Dimensional Lie Groups and Algebras, World Scientific, Singapore, 1998, pp. 22-46.
    • (1998) Analysis on Infinite-Dimensional Lie Groups and Algebras , pp. 22-46
    • Berezansky, Yu.M.1
  • 5
    • 0038291338 scopus 로고    scopus 로고
    • Pascal measure on generalized functions and the corresponding generalized Meixner polynomials
    • Yu.M. Berezansky, Pascal measure on generalized functions and the corresponding generalized Meixner polynomials, Methods Funct. Anal. Topology 8 (2002) 1-13.
    • (2002) Methods Funct. Anal. Topology , vol.8 , pp. 1-13
    • Berezansky, Yu.M.1
  • 11
    • 0038291335 scopus 로고
    • Pascal processes and their characterization
    • F.T. Bruss, L.C. Rogers, Pascal processes and their characterization, Stochastic Process. Appl. 37 (1991) 331-338.
    • (1991) Stochastic Process. Appl. , vol.37 , pp. 331-338
    • Bruss, F.T.1    Rogers, L.C.2
  • 13
    • 0011673479 scopus 로고
    • A biorthogonal analogy of the Hermite polynomials and the inversion of the Fourier transform with respect to a non-Gaussian measure
    • Yu.L. Daletsky, A biorthogonal analogy of the Hermite polynomials and the inversion of the Fourier transform with respect to a non-Gaussian measure, Funct. Anal. Appl. 25 (1991) 68-70.
    • (1991) Funct. Anal. Appl. , vol.25 , pp. 68-70
    • Daletsky, Yu.L.1
  • 15
    • 0003196608 scopus 로고
    • Complex Analysis in Locally Convex Spaces
    • North-Holland, Amsterdam
    • S. Dineen, Complex Analysis in Locally Convex Spaces, in: Mathematical Studies, Vol. 57, North-Holland, Amsterdam, 1981.
    • (1981) Mathematical Studies , vol.57
    • Dineen, S.1
  • 16
    • 0038518730 scopus 로고    scopus 로고
    • Processes of Meixner type
    • B. Grigelionis, Processes of Meixner type, Lithuanian Math. J. 39 (1999) 33-41.
    • (1999) Lithuanian Math. J. , vol.39 , pp. 33-41
    • Grigelionis, B.1
  • 18
    • 0037615776 scopus 로고    scopus 로고
    • On biorthogonal approach to a construction of non-Gaussian analysis and application to the Poisson analysis on the configuration space
    • N.A. Kachanovsky, On biorthogonal approach to a construction of non-Gaussian analysis and application to the Poisson analysis on the configuration space, Methods Funct. Anal. Topology 6 (2) (2000) 13-21.
    • (2000) Methods Funct. Anal. Topology , vol.6 , Issue.2 , pp. 13-21
    • Kachanovsky, N.A.1
  • 25
    • 0002300055 scopus 로고
    • Multiple Wiener integrals and non-Gaussian white noises: A Jacobi field approach
    • E.W. Lytvynov, Multiple Wiener integrals and non-Gaussian white noises: a Jacobi field approach, Methods Func. Analy. Topology 1 (1995) 61-85.
    • (1995) Methods Func. Analy. Topology , vol.1 , pp. 61-85
    • Lytvynov, E.W.1
  • 26
    • 84960600688 scopus 로고
    • Orthogonale Polynomsysteme mit einem besonderen Gestalt der erzeugenden Funktion
    • J. Meixner, Orthogonale Polynomsysteme mit einem besonderen Gestalt der erzeugenden Funktion, J. London Math. Soc. 9 (1934) 6-13.
    • (1934) J. London Math. Soc. , vol.9 , pp. 6-13
    • Meixner, J.1
  • 27
    • 0003866690 scopus 로고    scopus 로고
    • Chaotic and predictable representations for Lévy processes
    • D. Nualart, W. Schoutens, Chaotic and predictable representations for Lévy processes, Stochastic Process. Appl. 90 (2000) 109-122.
    • (2000) Stochastic Process. Appl. , vol.90 , pp. 109-122
    • Nualart, D.1    Schoutens, W.2
  • 28
    • 0003291564 scopus 로고    scopus 로고
    • Stochastic Processes and Orthogonal Polynomials
    • Springer, New York
    • W. Schoutens, Stochastic Processes and Orthogonal Polynomials, in: Lecture Notes in Statistics, Vol. 146, Springer, New York, 2000.
    • (2000) Lecture Notes in Statistics , vol.146
    • Schoutens, W.1
  • 30
    • 0035840456 scopus 로고    scopus 로고
    • An infinite-dimensional analogue of the Lebesgue measure and distinguished properties of the gamma process
    • N. Tsilevich, A. Vershik, M. Yor, An infinite-dimensional analogue of the Lebesgue measure and distinguished properties of the gamma process, J. Funct. Anal. 185 (2001) 274-296.
    • (2001) J. Funct. Anal. , vol.185 , pp. 274-296
    • Tsilevich, N.1    Vershik, A.2    Yor, M.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.