White Noise Calculus and Fock Space
Obata, Nobuaki.
White Noise Calculus and Fock Space [electronic resource] / by Nobuaki Obata. - X, 190 p. online resource. - Lecture Notes in Mathematics, 1577 0075-8434 ; . - Lecture Notes in Mathematics, 1577 .
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.
9783540484110
10.1007/BFb0073952 doi
Global analysis (Mathematics).
Distribution (Probability theory.
Analysis.
Theoretical, Mathematical and Computational Physics.
Probability Theory and Stochastic Processes.
QA299.6-433
515
White Noise Calculus and Fock Space [electronic resource] / by Nobuaki Obata. - X, 190 p. online resource. - Lecture Notes in Mathematics, 1577 0075-8434 ; . - Lecture Notes in Mathematics, 1577 .
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.
9783540484110
10.1007/BFb0073952 doi
Global analysis (Mathematics).
Distribution (Probability theory.
Analysis.
Theoretical, Mathematical and Computational Physics.
Probability Theory and Stochastic Processes.
QA299.6-433
515