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CONDITIONAL FOURIER-FEYNMAN TRANSFORM AND CONVOLUTION PRODUCT OVER WIENER PATHS IN ABSTRACT WIENER SPACE: AN Lp THEORY
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 Title & Authors
CONDITIONAL FOURIER-FEYNMAN TRANSFORM AND CONVOLUTION PRODUCT OVER WIENER PATHS IN ABSTRACT WIENER SPACE: AN Lp THEORY
Cho, Dong-Hyun;
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 Abstract
In this paper, using a simple formula, we evaluate the conditional Fourier-Feynman transforms and the conditional convolution products of cylinder type functions, and show that the conditional Fourier-Feynman transform of the conditional convolution product is expressed as a product of the conditional Fourier-Feynman transforms. Also, we evaluate the conditional Fourier-Feynman transforms of the functions of the forms exp {∫sub o/ (s,(s))ds}, exp{∫sub o/ (s,(s))ds}((T)), exp{∫sub o/ (s,(s))dζ(s)}, exp{∫sub o/ (s,(s))dζ(s)}((T)) which are of interest in Feynman integration theories and quantum mechanics.ics.ጊ缀Ѐ㘰〻Ԁ䭃䑎䷙᜕౼6㈰⸳㬅K䍄乍숗ᔌꄀ؀㘲ㄮ㠻Ԁ䭃䑎䴀
 Keywords
conditional analytic Feynman integral;conditional convolution product;conditional Fourier-Feynman transform;conditional Wiener integral;cylinder type function;simple formula for conditional Wiener integral;
 Language
English
 Cited by
1.
CONDITIONAL FOURIER-FEYNMAN TRANSFORMS OF VARIATIONS OVER WIENER PATHS IN ABSTRACT WIENER SPACE,;

대한수학회지, 2006. vol.43. 5, pp.967-990 crossref(new window)
2.
Conditional Integral Transforms on a Function Space,;

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A TIME-INDEPENDENT CONDITIONAL FOURIER-FEYNMAN TRANSFORM AND CONVOLUTION PRODUCT ON AN ANALOGUE OF WIENER SPACE,;

호남수학학술지, 2013. vol.35. 2, pp.179-200 crossref(new window)
4.
CONDITIONAL FOURIER-FEYNMAN TRANSFORMS AND CONVOLUTIONS OF UNBOUNDED FUNCTIONS ON A GENERALIZED WIENER SPACE,;

대한수학회지, 2013. vol.50. 5, pp.1105-1127 crossref(new window)
5.
CONDITIONAL INTEGRAL TRANSFORMS AND CONVOLUTIONS OF BOUNDED FUNCTIONS ON AN ANALOGUE OF WIENER SPACE,;

충청수학회지, 2013. vol.26. 2, pp.323-342 crossref(new window)
1.
CONDITIONAL FOURIER-FEYNMAN TRANSFORMS AND CONVOLUTIONS OF UNBOUNDED FUNCTIONS ON A GENERALIZED WIENER SPACE, Journal of the Korean Mathematical Society, 2013, 50, 5, 1105  crossref(new windwow)
2.
A TIME-INDEPENDENT CONDITIONAL FOURIER-FEYNMAN TRANSFORM AND CONVOLUTION PRODUCT ON AN ANALOGUE OF WIENER SPACE, Honam Mathematical Journal, 2013, 35, 2, 179  crossref(new windwow)
3.
CONDITIONAL INTEGRAL TRANSFORMS AND CONVOLUTIONS OF BOUNDED FUNCTIONS ON AN ANALOGUE OF WIENER SPACE, Journal of the Chungcheng Mathematical Society, 2013, 26, 2, 323  crossref(new windwow)
4.
Conditional integral transforms and conditional convolution products on a function space, Integral Transforms and Special Functions, 2012, 23, 6, 405  crossref(new windwow)
5.
A TRANSLATION THEOREM FOR THE GENERALIZED FOURIER-FEYNMAN TRANSFORM ASSOCIATED WITH GAUSSIAN PROCESS ON FUNCTION SPACE, Journal of the Korean Mathematical Society, 2016, 53, 5, 991  crossref(new windwow)
6.
Analytic Feynman integrals of transforms of variation of cylinder type functions over Wiener paths in abstract Wiener space, Central European Journal of Mathematics, 2005, 3, 3, 475  crossref(new windwow)
7.
Conditional Integral Transforms on a Function Space, Kyungpook mathematical journal, 2012, 52, 4, 413  crossref(new windwow)
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