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• W2002644912 abstract "In the framework of white noise analysis a Gel'fand triple ( L )⊂(L 2 )⊂( L ) ∗ has been defined (e.g. Kubo and Yokoi, 1989), the space of smooth test functionals ( L ) and the space of Hida distributions ( L ) ∗ play some important roles. It has been shown (e.g. Yokoi, 1990) that a positive Hida distribution Φ is given by a positive measure ν Φ on the space of real tempered distributions L ∗ . Thus the space ( L 2 ) Φ  L 2 ( L ∗ ; B , ν Φ ) can be defined, where B is the Borel σ-algebra on L ∗ generated by the weak topology. The present article is concerned with a special choice of pre-Dirichlet forms with domain ( L ) on ( L 2 ) Φ which is a generalization of the energy form (Hida, Potthoff and Streit, 1988) and of the type ε(F)= Φ; ∑ j,k H j,k ·∂ j F·∂ k F ̄ , for each F ϵ( L ) and where ( H j,k ; j, k ϵ N 0 ) is a double sequence of test functionals satisfying some natural conditions. Some closability results are given in the last section under mild conditions." @default.
• W2002644912 created "2016-06-24" @default.
• W2002644912 creator A5030143091 @default.
• W2002644912 date "1991-12-01" @default.
• W2002644912 modified "2023-09-23" @default.
• W2002644912 title "Construction of a general class of Dirichlet forms in terms of white noise analysis" @default.
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• W2002644912 doi "https://doi.org/10.1016/0304-4149(91)90082-n" @default.
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