CONDITIONAL FOURIER-FEYNMAN TRANSFORM AND CONDITIONAL CONVOLUTION PRODUCT ASSOCIATED WITH INFINITE DIMENSIONAL CONDITIONING FUNCTION

CONDITIONAL FOURIER-FEYNMAN TRANSFORM AND CONDITIONAL CONVOLUTION PRODUCT ASSOCIATED WITH INFINITE DIMENSIONAL CONDITIONING FUNCTION

In this paper, we use an infinite dimensional conditioning function to define a conditional Fourier-Feynman transform (CFFT) and a conditional convolution product (CCP) on the Wiener space. We establish the existences of the CFFT and the CCP for bounded functions which form a Banach algebra. We then...

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Veröffentlicht in:Taehan Suhakhoe hoebo 2023, Vol.60 (5), p.1221-1235
Hauptverfasser: Jae Gil Choi, Sang Kil Shim
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description In this paper, we use an infinite dimensional conditioning function to define a conditional Fourier-Feynman transform (CFFT) and a conditional convolution product (CCP) on the Wiener space. We establish the existences of the CFFT and the CCP for bounded functions which form a Banach algebra. We then provide fundamental relationships between the CFFTs and the CCPs.
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title CONDITIONAL FOURIER-FEYNMAN TRANSFORM AND CONDITIONAL CONVOLUTION PRODUCT ASSOCIATED WITH INFINITE DIMENSIONAL CONDITIONING FUNCTION
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