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White Noise Calculus and Fock Space

  • Authors
  • NobuakiĀ Obata

Part of the Lecture Notes in Mathematics book series (LNM, volume 1577)

Table of contents

  1. Front Matter
    Pages i-x
  2. Nobuaki Obata
    Pages 1-18
  3. Nobuaki Obata
    Pages 19-32
  4. Nobuaki Obata
    Pages 33-70
  5. Nobuaki Obata
    Pages 71-108
  6. Nobuaki Obata
    Pages 109-150
  7. Nobuaki Obata
    Pages 151-166
  8. Back Matter
    Pages 167-186

About this book

Introduction

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.

Keywords

calculus distribution functional analysis harmonic analysis operator operator theory

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0073952
  • Copyright Information Springer-Verlag Berlin Heidelberg 1994
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-57985-4
  • Online ISBN 978-3-540-48411-0
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site