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The Hilbert Space of Double Fourier Coefficients for an Abstract Wiener Space [PDF]

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 [PDF]

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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Towards Abstract Wiener Model Spaces [PDF]

, 2023
Implemented reviewer feedback, slightly changed formatting, corrected typos ...
Gideon Chiusole, Peter K. Friz
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CONDITIONAL FIRST VARIATION OVER WIENER PATHS IN ABSTRACT WIENER SPACE [PDF]

Journal of the Korean Mathematical Society, 2005
Summary: In this paper, we define the conditional first variation over Wiener paths in an abstract Wiener space and investigate its properties. Using these properties, we also investigate relationships among first variation, conditional first variation, Fourier-Feynman transform and conditional Fourier-Feynman transforms of functions in a Banach ...
Dong Hyun Cho
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The Wiener Closure Theorems for Abstract Wiener Spaces [PDF]

Proceedings of the American Mathematical Society, 1972
We introduce Y' and Y2 translates for functions in Y'1(a) and Y2(1i) where y is a Gaussian measure on a Banach space. With these translates and the Fourier-Wiener transforms defined by Cameron and Martin we obtain Wiener's closure theorem in Y2(u) and in Y1(p).
J. Kuelbs, V. Mandrekar
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Conditional Analytic Feynman Integral over Product Space of Wiener Paths in Abstract Wiener Space [PDF]

Rocky Mountain Journal of Mathematics, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dong Hyun Cho
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Convolution and the Fourier-Wiener Transform on Abstract Wiener Space [PDF]

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.
Il Yoo
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Diffusion semigroups on abstract Wiener space [PDF]

Transactions of the American Mathematical Society, 1972
The existence of a semigroup of solution operators associated with a second order infinite dimensional parabolic equation of the form ∂ u / ∂ t = L x u \partial u/\partial t = {L_x}u was previously established by the ...
M. Ann Piech
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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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Interpolation Theory on Sobolev Spaces over the Abstract Wiener Space [PDF]

Tokyo Journal of Mathematics, 1989
In recent years, the theory of Sobolev spaces over the abstract Wiener space was constructed in the study of stochastic differential equations ([9, 11, 15]). In the present paper, we prove an interpolation theorem on Sobolev spaces over the abstract Wiener space.
Takuya Sobukawa
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