Unitarity of Kuo's Fourier-Mehler transform

Un Cig Ji, Nobuaki Obata

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

Kuo's Fourier-Mehler transforms {Fθ} form a one-parameter automorphism group of the space of white noise distributions W*. The adjoint transforms {Gθ = Fθ*} form a one-parameter automorphism group of the space of test white noise functions W but do not admit unitary extensions with respect to the L2-norm induced from the Gaussian measure with variance 1. We prove that {G θ} admits an extension to a one-parameter group of unitary operators on the L2-space with respect to the Gaussian measure with variance 1/2.

Original languageEnglish
Pages (from-to)147-154
Number of pages8
JournalInfinite Dimensional Analysis, Quantum Probability and Related Topics
Volume7
Issue number1
DOIs
Publication statusPublished - 2004 Mar

Keywords

  • Fourier transform
  • Fourier-Mehler transform
  • Gaussian space
  • Generalized white noise functional
  • White noise

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Mathematical Physics
  • Applied Mathematics

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