White Noise Calculus and Fock Space

1. Front Matter

   Pages i-x

   PDF

2. Prerequisites

   • Nobuaki Obata

   Pages 1-18

3. White noise space

   • Nobuaki Obata

   Pages 19-32

4. White noise functionals

   • Nobuaki Obata

   Pages 33-70

5. Operator theory

   • Nobuaki Obata

   Pages 71-108

6. Toward harmonic analysis

   • Nobuaki Obata

   Pages 109-150

7. Addendum

   • Nobuaki Obata

   Pages 151-166

8. Back Matter

   Pages 167-186

   PDF

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.

• calculus
• distribution
• functional analysis
• harmonic analysis
• operator
• operator theory