The Segal-Bargmann transform for Lévy functionals

DOI10.1006/jfan.1999.3452zbMath0952.60069OpenAlexW2065868493MaRDI QIDQ1125281

Yuh-Jia Lee, Hsin-Hung Shih

Publication date: 2 January 2001

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.1999.3452

zbMATH Keywords

white noiseLévy functionalsS-transformSegal-Bergmann spaceU-transform

Mathematics Subject Classification ID

Integral transforms in distribution spaces (46F12) White noise theory (60H40) Distributions on infinite-dimensional spaces (46F25)

Related Items (16)

Spectral integrals of Bernoulli generalized functionals ⋮ Convergence theorems for generalized functional sequences of discrete-time normal martingales ⋮ Generalized weighted number operators on functionals of discrete-time normal martingales ⋮ Holomorphic functions and the Itô chaos ⋮ A characterization of operators on functionals of discrete-time normal martingales ⋮ UNITARY REPRESENTATIONS OF THE WITT AND sl(2, ℝ)-ALGEBRAS THROUGH RENORMALIZED POWERS OF THE QUANTUM PASCAL WHITE NOISE ⋮ Characterization theorems for generalized functionals of discrete-time normal martingale ⋮ The Segal-Bargmann transform for Lévy white noise functionals associated with non-integrable Lévy processes ⋮ Convergence theorems for operators sequences on functionals of discrete-time normal martingales ⋮ Nuclear Realization of Virasoro–Zamolodchikov-w_∞⋆-Lie Algebras Through the Renormalized Higher Powers of Quantum Meixner White Noise ⋮ AN APPLICATION OF THE SEGAL–BARGMANN TRANSFORM TO THE CHARACTERIZATION OF LÉVY WHITE NOISE MEASURES ⋮ Lévy white noise measures on infinite-dimensional spaces: existence and characterization of the measurable support ⋮ Pascal white noise calculus ⋮ Analysis of generalized Lévy white noise functionals ⋮ Lévy white noise calculus based on interaction exponents ⋮ A generalised Itō formula for Lévy-driven Volterra processes

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• Multiple Wiener integral
• Spectral Type of the Shift Transformation of Differential Processes With Stationary Increments
• Analysis on Poisson and Gamma Spaces
• Chaotic and variational calculus in discrete and continuous time for the poisson process

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