White noise calculus and Fock space

Nobuaki Obata

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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[目次]

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

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この本の情報

書名 White noise calculus and Fock space
著作者等 尾畑 伸明
Obata Nobuaki
書名別名 Fock space
シリーズ名 Lecture notes in mathematics
出版元 Springer-Verlag
刊行年月 c1994
ページ数 ix, 183 p.
大きさ 24 cm
ISBN 0387579850
3540579850
NCID BA22763349
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言語 英語
出版国 ドイツ
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