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Fourier-Feynman transforms of unbounded functionals on abstract Wiener space

Byoung Kim;  Il Yoo;  Dong Cho — 2010

Open Mathematics

Huffman, Park and Skoug established several results involving Fourier-Feynman transform and convolution for functionals in a Banach algebra S on the classical Wiener space. Chang, Kim and Yoo extended these results to abstract Wiener space for a more generalized Fresnel class ℱ 𝒜 1 , 𝒜 2 A1,A2 than the Fresnel class ℱ (B)which corresponds to the Banach algebra S. In this paper we study Fourier-Feynman transform, convolution and first variation of unbounded functionals on abstract Wiener space having the form...

Evaluation formulas for a conditional Feynman integral over Wiener paths in abstract Wiener space

Kun Soo Chang;  Dong Hyun Cho;  Il Yoo — 2004

Czechoslovak Mathematical Journal

In this paper, we introduce a simple formula for conditional Wiener integrals over C 0 ( 𝔹 ) , the space of abstract Wiener space valued continuous functions. Using this formula, we establish various formulas for a conditional Wiener integral and a conditional Feynman integral of functionals on C 0 ( 𝔹 ) in certain classes which correspond to the classes of functionals on the classical Wiener space introduced by Cameron and Storvick. We also evaluate the conditional Wiener integral and conditional Feynman integral...

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