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Cylinder functions in the Fresnel class of functions on abstract Wiener spaces

Authors: Dong Myung Chung and Hong Taek Hwang
Journal: Proc. Amer. Math. Soc. 115 (1992), 381-388
MSC: Primary 28C20; Secondary 46G12
MathSciNet review: 1097340
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Abstract: In this paper we consider the class of cylinder functions on abstract Wiener space $ B$ and give necessary and sufficient conditions of cylinder functions on $ B$ to be in the Banach algebra $ \mathfrak{F}\left( B \right)$ (resp. $ {\mathfrak{F}^*}\left( B \right)$) of analytic (resp. sequential) Feynman integrable functions on $ B$. The results here subsume similar known results obtained by Chang, Johnson, and Skoug in the setting of Hilbert and Wiener spaces.

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