White Noise Calculus is a distribution theory on Gaussian space, proposed by T. Hida in 1975. This approach enables us to use pointwise defined creation and annihilation operators as well as the well-established theory of nuclear space.This self-contained monograph presents, for the first time, a systematic introduction to operator theory on fock space by means of white noise calculus. The goal is a comprehensive account of general expansion theory of Fock space operators and its applications. In particular,first order differential operators, Laplacians, rotation group, Fourier transform and their interrelations are discussed in detail w.r.t. harmonic analysis on Gaussian space. The mathematical formalism used here is based on distribution theory and functional analysis , prior knowledge of white noise calculus is not required.

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Bibliographic Information

Book Title: White Noise Calculus and Fock Space
Authors: Nobuaki Obata
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/BFb0073952
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1994
Softcover ISBN: 978-3-540-57985-4Published: 27 May 1994
eBook ISBN: 978-3-540-48411-0Published: 15 November 2006
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: X, 190
Topics: Analysis, Theoretical, Mathematical and Computational Physics, Probability Theory and Stochastic Processes

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Table of contents (6 chapters)

Front Matter

Prerequisites

White noise space

White noise functionals

Operator theory

Toward harmonic analysis

Addendum

Back Matter

About this book