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April, 2004 A role of Bargmann-Segal spaces in characterization and expansion of operators on Fock space
Un Cig JI, Nobuaki OBATA
J. Math. Soc. Japan 56(2): 311-338 (April, 2004). DOI: 10.2969/jmsj/1191418632


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.


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Un Cig JI. Nobuaki OBATA. "A role of Bargmann-Segal spaces in characterization and expansion of operators on Fock space." J. Math. Soc. Japan 56 (2) 311 - 338, April, 2004.


Published: April, 2004
First available in Project Euclid: 3 October 2007

zbMATH: 1087.46022
MathSciNet: MR2048461
Digital Object Identifier: 10.2969/jmsj/1191418632

Primary: 46G20
Secondary: 46F25 , 60H40 , 81S25

Keywords: Bargmann-Segal space , chaotic expansion , Fock space , Gaussian analysis , integral kernel operator , operator symbol , quantum stochastic differential equation , white noise differential equation

Rights: Copyright © 2004 Mathematical Society of Japan


Vol.56 • No. 2 • April, 2004
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