FOURIER-FEYNMAN TRANSFORMS FOR FUNCTIONALS IN A GENERALIZED FRESNEL CLASS

Title & Authors
FOURIER-FEYNMAN TRANSFORMS FOR FUNCTIONALS IN A GENERALIZED FRESNEL CLASS
Yoo, Il; Kim, Byoung-Soo;

Abstract
Huffman, Park and Skoug introduced various results for the $\small{L_p}$ analytic Fourier-Feynman transform and the convolution for functionals on classical Wiener space which belong to some Banach algebra S introduced by Cameron and Strovic. Also Chang, Kim and Yoo extended the above results to an abstract Wiener space for functionals in the Fresnel class F(B) which corresponds to S. Recently Kim, Song and Yoo investigated more generalized relationships between the Fourier-Feynman transform and the convolution product for functionals in a generalized Fresnel class $\small{F_{A_1,A`_2}}$ containing F(B). In this paper, we establish various interesting relationships and expressions involving the first variation and one or two of the concepts of the Fourier-Feynman transform and the convolution product for functionals in $\small{F_{A_1,A_2}}$.
Keywords
abstract Wiener space;generalized Fresnel class;analytic Feynman integral;Fourier-Feynman transform;convolution;first variation;
Language
English
Cited by
1.
FOURIER-FEYNMAN TRANSFORMS FOR FUNCTIONALS IN A GENERALIZED FRESNEL CLASS,;;

대한수학회논문집, 2007. vol.22. 1, pp.75-90
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