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

심상길|최재길
대한수학회 (The Korean Mathematical Society)|2023.09|대한수학회보 (Bulletin of the KMS)|제60권 제5호|pp. 1221-1235|DOI 10.4134/BKMS.b220602

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참고문헌

키워드

Wiener spaceconditional convolution productconditional Fourier–Feynman transformPaley–Wiener–Zygmund stochastic integral
주제분류수학

초록

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.

Abstract

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.

참고문헌 (16)

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관련 논문AI추천

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