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장승준,정현수 충청수학회 2008 충청수학회지 Vol.21 No.2
In this paper, we use a generalized Brownian motion process to define a generalized analytic Feynman integral. We then establish several integration formulas for generalized analytic Feynman integrals, generalized analytic Fourier-Feynman transforms and generalized integral transforms of functionals in the class of functionals E0. Finally, we use these integration formulas to obtain several generalized Feynman integrals involving the gen-eralized analytic Fourier-Feynman transform and the generalized integral transform of functionals in E0.
INTEGRAL TRANSFORMS AND INVERSE INTEGRAL TRANSFORMS WITH RELATED TOPICS ON FUNCTION SPACE I
장승준,정현수 한국수학교육학회 2009 純粹 및 應用數學 Vol.16 No.4
In this paper we establish various relationships among the generalized integral transform, the generalized convolution product and the ¯rst variation for functionals in a Banach algebra [수식] introduced by Chang and Skoug in [14]. We then derive an inverse integral transform and obtain several relationships involving inverse integral transforms.
A FRESNEL TYPE CLASS ON FUNCTION SPACE
장승준,최재길,이상덕 한국수학교육학회 2009 純粹 및 應用數學 Vol.16 No.1
In this paper we define a Banach algebra on very general function space induced by a generalized Brownian motion process rather than on Wiener space, but the Banach algebra can be considered as a generalization of Fresnel class defined on Wiener space. We then show that several interesting functions in quantum mechanic are elements of the class.
ADMIXABLE OPERATORS AND A TRANSFORM SEMIGROUP ON ABSTRACT WIENER SPACE
장승준,최재길,David Skoug 대한수학회 2015 대한수학회지 Vol.52 No.1
The purpose of this paper is first of all to investigate the behavior of admixable operators on the product of abstract Wiener spaces and secondly to examine transform semigroups which consist of admix- Wiener transforms on abstract Wiener spaces.
Generalized analytic Feynman integral via function space integral of bounded cylinder functionals
장승준,최재길,정현수 대한수학회 2011 대한수학회보 Vol.48 No.3
In this paper, we use a generalized Brownian motion to define a generalized analytic Feynman integral. We then obtain some results for the generalized analytic Feynman integral of bounded cylinder functionals of the form F(x)=[기호](( g_1, x)^~, ....., (g_n, x)^~) defined on a very general function space C_(a,b)[0,T]. We also present a change of scale formula for function space integrals of such cylinder functionals.
장승준,최재길 대한수학회 2004 대한수학회보 Vol.41 No.1
In [10], Chang and Skoug used a generalized Brownianmotion process to define a generalized analytic Feynman integraland a generalized analytic Fourier-Feynman transform. In thispaper we define the conditional generalized Fourier-Feynmantransform and conditional generalized convolution product onfunction space. We then establish some relationships between theconditional generalized Fourier-Feynman transform and conditionalgeneralized convolution product for functionals on function spacethat belonging to a Banach algebra.
함수공간에서의 일반화된 푸리에-파인만 변환에 관한 고찰
장승준,Chang, Seung-Jun 한국수학사학회 2007 Journal for history of mathematics Vol.20 No.3
본 논문은 일반화된 브라운 확률과정으로 유도된 함수공간에서 정의되는 일반화된 파인만 적분과 일반화된 푸리에-파인만 변환을 소개하고, 이들의 존재정리 및 여러 가지 성질을 설명한다. 그리고 푸리에 변환과 일반화된 해석적 푸리에-파인만 변환의 유사성을 조사한다. In this paper, we define a generalized Feynman integral and a generalized Fourier-Feynman transform on function space induced by generalized Brownian motion process. We then give existence theorems and several properties for these concepts. Finally we investigate relationships of the Fourier transform and the generalized Fourier-Feynman transform.
장승준,최재길 대한수학회 2018 대한수학회지 Vol.55 No.1
In this article, we establish translation theorems for the analytic Fourier--Feynman transform of functionals in non-stationary Gaussian processes on Wiener space. We then proceed to show that these general translation theorems can be applied to two well-known classes of functionals; namely, the Banach algebra $\mathcal S$ introduced by Cameron and Storvick, and the space $\mathcal B_{\mathcal A}^{(p)}$ consisting of functionals of the form $F(x)=f(\langle{\alpha_1,x}\rangle,\ldots,\langle{\alpha_n,x}\rangle)$, where $\langle{\alpha,x}\rangle$ denotes the Paley--Wiener--Zygmund stochastic integral $\int_0^T \alpha(t)dx(t)$.