A role of bargmann-segal spaces in characterization and expansion of operators on Fock space

Un Cig Ji, Nobuaki Obatay

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

A rigged Hilbert space formalism is introduced to study Fock space operators. The symbols of continuous operators on a rigged Fock space are characterized in terms of Bargmann-Segal spaces and complex Gaussian integrals. In particular, characterizations of bounded operators and of operators of Hilbert-Schmidt class on the middle Fock space are obtained. As an application we establish an operator version of chaotic expansion (Wiener-Itô expansion) and describe a relation to the Fock expansion in terms of the Wick exponential of the number operator. As another application we discuss regularity property of a solution to a normal-ordered white noise differential equation generalizing a quantum stochastic differential equation.

Original languageEnglish
Pages (from-to)311-338
Number of pages28
JournalJournal of the Mathematical Society of Japan
Volume56
Issue number2
DOIs
Publication statusPublished - 2004

Keywords

  • Bargmann-Segal space
  • Chaotic expansion
  • Fock space
  • Gaussian analysis
  • Integral kernel operator
  • Operator symbol
  • Quantum stochastic differential equation
  • White noise differential equation

ASJC Scopus subject areas

  • Mathematics(all)

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