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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

First order differential operators
in white noise analysis


Authors: Dong Myung Chung and Tae Su Chung
Journal: Proc. Amer. Math. Soc. 126 (1998), 2369-2376
MSC (1991): Primary 46F25
DOI: https://doi.org/10.1090/S0002-9939-98-04323-8
MathSciNet review: 1451792
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Abstract: Let $(E)$ be the space of test white noise functionals. We first introduce a family $ \{ \diamond _{\gamma}\,\,;\,\,\gamma\in {\Bbb C} \} $ of products on $(E)$ including Wiener and Wick products, and then show that with each product $\diamond _{\gamma}$, we can associate a first order differential operator, called a first order $\gamma$-differential operator. We next show that a first order $\gamma$-differential operator is indeed a continuous derivation under the product $\diamond _{\gamma}$. We finally characterize $\gamma\Delta _G+N$ by means of rotation-invariance and continuous derivation under the product $\diamond _{\gamma}$. Here $\Delta _G$ and $N$ are the Gross Laplacian and the number operator on $(E)$, respectively.


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Additional Information

Dong Myung Chung
Affiliation: Department of Mathematics, Sogang University Seoul, 121-742, Korea
Email: dmchung@ccs.sogang.ac.kr

Tae Su Chung
Affiliation: Department of Mathematics, Sogang University Seoul, 121-742, Korea

DOI: https://doi.org/10.1090/S0002-9939-98-04323-8
Received by editor(s): January 21, 1997
Additional Notes: Research supported by KOSEF 996-0100-00102 and BSRI 97-1412.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society