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The Hilbert Space of Double Fourier Coefficients for an Abstract Wiener Space
Mathematics, 2021 Fourier series is a well-established subject and widely applied in various fields. However, there is much less work on double Fourier coefficients in relation to spaces of general double sequences.
Jeong-Gyoo Kim
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Integrability on the Abstract Wiener Space of Double Sequences and Fernique Theorem
Journal of Function Spaces, 2021 The integrability of a function defined on the abstract Wiener space of double Fourier coefficients is explored. The abstract Wiener space is also a Hilbert space.
Jeong-Gyoo Kim
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A change of scale formula for Wiener integrals on abstract Wiener spaces [PDF]
International Journal of Mathematics and Mathematical Sciences, 1994 In this paper we obtain a change of scale formula for Wiener integrals on abstract Wiener spaces. This formula is shown to hold for many classes of functions of interest in Feynman integration theory and quantum mechanics.
Il Yoo, David Skoug
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A change of scale formula for Wiener integrals of cylinder functions on abstract Wiener space
International Journal of Mathematics and Mathematical Sciences, 1998 The purpose of this paper is to establish the existence of analytic Wiener and Feynman integrals for a class of certain cylinder functions which is of the form: F(x)=f((h1,x)∼,⋯,(hn,x)∼), x∈B, on the abstract Wiener space, and to establish the ...
Young Sik Kim
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Convolution and the Fourier-Wiener Transform on Abstract Wiener Space
Rocky Mountain Journal of Mathematics, 1995 \textit{J. Yeh} [Pac. J. Math. 15, 731-738 (1965; Zbl 0128.33702)] calculated the convolution and its Fourier-Wiener transform for certain classes of functionals defined on classical Wiener spaces. In the paper under review, this result is extended to functionals defined on abstract Wiener spaces.
I. Yoo
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The Construction of Filtrations on Abstract Wiener Space
Journal of Functional Analysis, 1997 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Uuml;stünel, A.S., Zakai, M.
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Embedding the Abstract Wiener Space in a Probability Space
Journal of Functional Analysis, 2000 Consider an abstract Wiener process \((W,w,H)\), embedded in a probability space \((\Omega,{\mathcal F},\mathbb{P})\), in the sense that \(w\) is a \(W\)-valued Gaussian variable, with \(H\) as reproducing space. On the one hand, a simple conditional Malliavin calculus is defined, by differentiating only in the direction of \(w\). On the other hand, an
Üstünel, A.S., Zakai, M.
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Stochastic integrals in abstract Wiener space [PDF]
Pacific Journal of Mathematics, 1972 H. Kuo
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CHANGE OF SCALE FORMULAS FOR WIENER INTEGRAL OVER PATHS IN ABSTRACT WIENER SPACE [PDF]
Communications of the Korean Mathematical Society, 2006 Summary: Wiener measure and Wiener measurability behave bad-ly under the change of scale transformation. We express the analytic Feynman integral over \(C_0(B)\) as a limit of Wiener integrals over \(C_0(B)\) and establish change of scale formulas for Wiener integrals over \(C_0(B)\) for some functionals.
Kim, Byoung Soo, Kim, Tae Soo
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Abstract Wiener space, revisited
Communications on Stochastic Analysis, 2008 D. Stroock
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