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Generalized Fourier--Feynman transforms and convolutions for exponential type functions of generalized Brownian motion paths

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대한수학회 (The Korean Mathematical Society)|2023.10|대한수학회논문집 (Communications of the KMS)|제38권 제4호|pp. 1141-1151|DOI 10.4134/CKMS.c230005

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키워드

Generalized Brownian motion processgeneralized Fourier--Feynman transformgeneralized convolution productexponential type function
주제분류수학

초록

Let $C_{a,b}[0,T]$ denote the space of continuous sample paths of a generalized Brownian motion process (GBMP). In this paper, we study the structures which exist between the analytic generalized Fourier--Feynman transform (GFFT) and the generalized convolution product (GCP) for functions on the function space $C_{a,b}[0,T]$. For our purpose, we use the exponential type functions on the general Wiener space $C_{a,b}[0,T]$. The class of all exponential type functions is a fundamental set in \linebreak $L_2(C_{a,b}[0,T])$.

Abstract

Let $C_{a,b}[0,T]$ denote the space of continuous sample paths of a generalized Brownian motion process (GBMP). In this paper, we study the structures which exist between the analytic generalized Fourier--Feynman transform (GFFT) and the generalized convolution product (GCP) for functions on the function space $C_{a,b}[0,T]$. For our purpose, we use the exponential type functions on the general Wiener space $C_{a,b}[0,T]$. The class of all exponential type functions is a fundamental set in \linebreak $L_2(C_{a,b}[0,T])$.

참고문헌 (22)

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