Operator calculus on vector-valued white noise functionals

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10 Citations (Scopus)

Abstract

A general theory of operators on vector-valued white noise functionals is established in line with Hid′s white noise calculus. A basic role is played by an integral kernel operator which is a superposition of creation and annihilation operators with operator-valued distributions as integral kernel. The symbol of a continuous operator on vector-valued white noise functionals is characterized by its analyticity and boundedness. A significant consequence is that every continuous operator on vector-valued white noise functionals admits an infinite series expansion in terms of integral kernel operators with precise estimate of the convergence.

Original languageEnglish
Pages (from-to)185-232
Number of pages48
JournalJournal of Functional Analysis
Volume121
Issue number1
DOIs
Publication statusPublished - 1994 Apr
Externally publishedYes

ASJC Scopus subject areas

  • Analysis

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