-function of an operator: A white noise approach

Authors:
Caishi Wang, Zhiyuan Huang and Xiangjun Wang

Journal:
Proc. Amer. Math. Soc. **133** (2005), 891-898

MSC (2000):
Primary 60H40

DOI:
https://doi.org/10.1090/S0002-9939-04-07769-X

Published electronically:
October 7, 2004

MathSciNet review:
2113941

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be the canonical framework of white noise analysis over the Gel'fand triple and be the space of continuous linear operators from to . Let be a self-adjoint operator in with spectral representation . In this paper, it is proved that under appropriate conditions upon , there exists a unique linear mapping such that for each . The mapping is then naturally used to define as , where is the Dirac -function. Finally, properties of the mapping are investigated and several results are obtained.

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Additional Information

**Caishi Wang**

Affiliation:
Department of Mathematics, Northwest Normal University, Lanzhou, Gansu 730070, People’s Republic of China

Email:
wangcs@nwnu.edu.cn

**Zhiyuan Huang**

Affiliation:
Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, People’s Republic of China

Email:
zyhuang@hust.edu.cn

**Xiangjun Wang**

Affiliation:
Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, People’s Republic of China

Email:
x.j.wang@yeah.net

DOI:
https://doi.org/10.1090/S0002-9939-04-07769-X

Keywords:
White noise analysis,
self-adjoint operator,
Schwartz generalized function

Received by editor(s):
December 10, 2002

Received by editor(s) in revised form:
September 16, 2003

Published electronically:
October 7, 2004

Communicated by:
Richard C. Bradley

Article copyright:
© Copyright 2004
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.