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A translation theorem for the generalized Fourier--Feynman transform associated with Gaussian process on function space

최재길|장승준|Ae Young Ko
대한수학회 (The Korean Mathematical Society)|2016.09|대한수학회지 (Journal of the KMS)|제53권 제5호|pp. 991-1017

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참고문헌

키워드

Gaussian processgeneralized Brownian motion processtranslation theoremgeneralized analytic Feynman integralgeneralized analytic Fourier--Feynman transform
주제분류수학

초록

In this paper we define a generalized analytic Fourier--Feyn\-man transform associated with Gaussian process on the function space $C_{a,b}[0,T]$. We establish the existence of the generalized analytic Fourier--Feynman transform for certain bounded functionals on $C_{a,b}[0,T]$. We then proceed to establish a translation theorem for the generalized transform associated with Gaussian process.

Abstract

In this paper we define a generalized analytic Fourier--Feyn\-man transform associated with Gaussian process on the function space $C_{a,b}[0,T]$. We establish the existence of the generalized analytic Fourier--Feynman transform for certain bounded functionals on $C_{a,b}[0,T]$. We then proceed to establish a translation theorem for the generalized transform associated with Gaussian process.

참고문헌 (32)

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