PROBABILITY MEASURES ON ℂ ARISING FROM THE JACOBI–SZEGÖ PARAMETERS FOR CONTINUOUS DUAL HAHN POLYNOMIALS

DOI10.1142/S0219025711004493zbMath1232.44007MaRDI QIDQ3095477

Nobuhiro Asai

Publication date: 2 November 2011

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

zbMATH Keywords

modified Bessel functionsMellin convolutioncontinuous dual Hahn polynomialsJacobi-Szegő parametershalf-Meixner distributionprobability measures on \(\mathbb C\)

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Noncommutative probability and statistics (46L53) Moment problems (44A60) Distribution theory (60E99)

Cites Work

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• Quantum Ito's formula and stochastic evolutions
• The classical moment problem as a self-adjoint finite difference operator
• Processes of Meixner type
• Generalized quantum stochastic processes on Fock space
• Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions
• WHITE NOISE LÉVY–MEIXNER PROCESSES THROUGH A TRANSFER PRINCIPAL FROM ONE-MODE TO ONE-MODE TYPE INTERACTING FOCK SPACES
• THE CONSTRUCTION OF SUBORDINATED PROBABILITY MEASURES ON ℂ ASSOCIATED WITH THE JACOBI–SZEGÖ PARAMETERS
• Calculus on Gaussian and Poisson white noises
• Some Hypergeometric Orthogonal Polynomials
• Interacting Fock Spaces and Gaussianization of Probability Measures
• Lévy processes, polynomials and martingales
• ANALYTIC CHARACTERIZATION OF ONE-MODE INTERACTING FOCK SPACE
• Segal-Bargmann transforms of one-mode interacting Fock spaces associated with Gaussian and Poisson measures
• HILBERT SPACE OF ANALYTIC FUNCTIONS ASSOCIATED WITH THE MODIFIED BESSEL FUNCTION AND RELATED ORTHOGONAL POLYNOMIALS

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