White Noise Calculus and Fock Space [electronic resource] / by Nobuaki Obata.

By:

Obata, Nobuaki [author.]

Contributor(s):

SpringerLink (Online service)

Material type: Text

TextSeries: Lecture Notes in Mathematics ; 1577Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1994Description: X, 190 p. online resourceContent type:

text

Media type:

computer

Carrier type:

online resource

ISBN:

9783540484110

Subject(s):

Additional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification:

515 23

LOC classification:

QA299.6-433

Online resources:

Click here to access online

Contents:

Prerequisites -- White noise space -- White noise functionals -- Operator theory -- Toward harmonic analysis -- Addendum.

In: Springer eBooksSummary: 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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Prerequisites -- White noise space -- White noise functionals -- Operator theory -- Toward harmonic analysis -- Addendum.

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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