Transformations for white noise functionals

Takeyuki Hida, Hui Hsiung Kuof, Nobuaki Obata

Research output: Contribution to journalArticle

34 Citations (Scopus)

Abstract

Several results concerning the spaces (E) and (E)* of test and generalized white noise functionals, respectively, are obtained. The irreducibility of the canonical commutation relation for operators on (E) and on (E)* is proved. It is shown that the Fourier-Mehler transform F0 on (E)* is the adjoint of a continuous linear operator G0 on (E). Moreover, a characterization theorem for the Fourier-Mehler transform is proved. In particular, the Fourier transform is the unique (up to a constant) continuous linear operator F on (E)* such that FD̃ξ = q̃ξF and Fq̃ξ = - D̃ξF. Here D̃ξ and q̃ξ are differentiation and multiplication operators, respectively. Several one-parameter transformation groups acting on (E) and the Lie algebra generated by their infinitesimal generators are also discussed.

Original languageEnglish
Pages (from-to)259-277
Number of pages19
JournalJournal of Functional Analysis
Volume111
Issue number2
DOIs
Publication statusPublished - 1993 Feb 1
Externally publishedYes

ASJC Scopus subject areas

  • Analysis

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