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FOCK FACTORIZATION OF B-VALUED ANALYTIC MAPPINGS ON A HILBERT INDUCTIVE LIMIT

Part of: Stochastic analysis

Published online by Cambridge University Press:  05 October 2009

CAISHI WANG ,
YULAN ZHOU ,
DECHENG FENG  and
QI HAN
CAISHI WANG*
Affiliation:
School of Mathematics and Information Science, Northwest Normal University, Lanzhou, Gansu 730070, PR China (email: wangcs@nwnu.edu.cn, cswangnwnu@163.com)
YULAN ZHOU
Affiliation:
School of Mathematics and Information Science, Northwest Normal University, Lanzhou, Gansu 730070, PR China (email: zhouylw@nwnu.edu.cn)
DECHENG FENG
Affiliation:
School of Mathematics and Information Science, Northwest Normal University, Lanzhou, Gansu 730070, PR China (email: fengdc@nwnu.edu.cn)
QI HAN
Affiliation:
School of Mathematics and Information Science, Northwest Normal University, Lanzhou, Gansu 730070, PR China (email: hanqi1978@nwnu.edu.cn)
*
✉For correspondence; e-mail: wangcs@nwnu.edu.cn, cswangnwnu@163.com
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Abstract

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Let 𝒩* be a Hilbert inductive limit and X a Banach space. In this paper, we obtain a necessary and sufficient condition for an analytic mapping Ψ:𝒩*↦X to have a factorization of the form Ψ=T∘ℰ, where ℰ is the exponential mapping on 𝒩* and T:Γ(𝒩*)↦X is a continuous linear operator, where Γ(𝒩*) denotes the Boson Fock space over 𝒩*. To prove this result, we establish some kernel theorems for multilinear mappings defined on multifold Cartesian products of a Hilbert space and valued in a Banach space, which are of interest in their own right. We also apply the above factorization result to white noise theory and get a characterization theorem for white noise testing functionals.

Keywords

inductive limitB-valued analytic mappingFock factorizationwhite noise

MSC classification

Secondary: 60H40: White noise theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 81 , Issue 2 , April 2010 , pp. 236 - 250
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

Footnotes

Supported by National Natural Science Foundation of China (10571065), Natural Science Foundation of Gansu Province (0710RJZA106) and NWNU-KJCXGC, PR China.

References

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[5]Obata, N., White Noise Calculus and Fock Space, Lecture Notes in Mathematics, 1577 (Springer, Berlin, 1994).CrossRefGoogle Scholar