Unitarity of generalized fourier-gauss transforms

Un Cig Ji, Nobuaki Obata

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

A generalized Fourier-Gauss transform is an operator acting in a Boson Fock space and is formulated as a continuous linear operator acting on the space of test white noise functions. It does not admit, in general, a unitary extension with respect to the norm of the Boson Fock space induced from the Gaussian measure with variance 1 but is extended to a unitary isomorphism if the Gaussian measure is replaced with the ones with different covariance operators. As an application, unitarity of a generalized dilation is discussed.

Original languageEnglish
Pages (from-to)733-751
Number of pages19
JournalStochastic Analysis and Applications
Volume24
Issue number4
DOIs
Publication statusPublished - 2006 Aug 1

Keywords

  • Boson Fock space
  • Fourier-Gauss transform
  • Generalized Fourier-Gauss transform
  • Generalized dilation
  • Kuo's Fourier transform
  • Unitarity
  • White noise theory

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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