Segal-Bargmann transforms of one-mode interacting Fock spaces associated with Gaussian and Poisson measures

DOI10.1090/S0002-9939-02-06564-4zbMath1028.46038arXivmath/0110011OpenAlexW1672620828MaRDI QIDQ4780420

Nobuhiro Asai, Izumi Kubo, Hui-Hsiung Kuo

Publication date: 19 November 2002

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0110011

zbMATH Keywords

Poisson measureGaussian measureSegal-Bargmann transforminteracting Fock space

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Hilbert spaces of continuous, differentiable or analytic functions (46E20) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)

Related Items (13)

Interpolations of Bargmann type measures ⋮ Hopf Structure for the q-Lévy-Meixner Oscillator Algebra ⋮ HILBERT SPACE OF ANALYTIC FUNCTIONS ASSOCIATED WITH THE MODIFIED BESSEL FUNCTION AND RELATED ORTHOGONAL POLYNOMIALS ⋮ WICK CALCULUS FOR THE SQUARE OF A GAUSSIAN RANDOM VARIABLE WITH APPLICATION TO YOUNG AND HYPERCONTRACTIVE INEQUALITIES ⋮ AN APPLICATION OF THE SEGAL–BARGMANN TRANSFORM TO THE CHARACTERIZATION OF LÉVY WHITE NOISE MEASURES ⋮ Quadratic harnesses, $q$-commutations, and orthogonal martingale polynomials ⋮ On stochastic differential equations driven by the renormalized square of the Gaussian white noise ⋮ Radial Bargmann representation for the Fock space of type B ⋮ PROBABILITY MEASURES ON ℂ ARISING FROM THE JACOBI–SZEGÖ PARAMETERS FOR CONTINUOUS DUAL HAHN POLYNOMIALS ⋮ THE CONSTRUCTION OF SUBORDINATED PROBABILITY MEASURES ON ℂ ASSOCIATED WITH THE JACOBI–SZEGÖ PARAMETERS ⋮ INTERPOLATION OF CHEBYSHEV POLYNOMIALS AND INTERACTING FOCK SPACES ⋮ THE BRENKE TYPE GENERATING FUNCTIONS AND EXPLICIT FORMS OF MRM-TRIPLES BY MEANS OF Q-HYPERGEOMETRIC SERIES ⋮ A HÖLDER INEQUALITY FOR NORMS OF POISSONIAN WICK PRODUCTS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Mathematical characterization of the physical vacuum for a linear Bose- Einstein field
• Quantum Ito's formula and stochastic evolutions
• Analytic version of test functionals, Fourier transform, and a characterization of measures in white noise calculus
• Finite dimensional Hida distributions
• Simple setting for white noise calculus using Bargmann space and Gauss transform
• On a Hilbert space of analytic functions and an associated integral transform part I
• Calculus on Gaussian and Poisson white noises
• A New Class of White Noise Generalized Functions
• Interacting Fock Spaces and Gaussianization of Probability Measures
• ROLES OF LOG-CONCAVITY, LOG-CONVEXITY, AND GROWTH ORDER IN WHITE NOISE ANALYSIS
• ANALYTIC CHARACTERIZATION OF ONE-MODE INTERACTING FOCK SPACE
• A q deformation of the Gauss distribution
• On a Hilbert Space of Analytie Functions and an Associated Integral Transform. Part II. A Family of Related Function Spaces Application to Distribution Theory
• Bell numbers, log-concavity, and log-convexity
• General characterization theorems and intrinsic topologies in white noise analysis

This page was built for publication: Segal-Bargmann transforms of one-mode interacting Fock spaces associated with Gaussian and Poisson measures