arXiv subjects

Seung Jun Chang

Publications and source records attributed to Seung Jun Chang.

4 recordsLinked to original sources

arXiv2019

Algebraic structure of the $L_2$ analytic Fourier-Feynman transform associated with Gaussian processes on Wiener space

In this paper we study algebraic structures of the classes of the $L_2$ analytic Fourier-Feynman transforms on Wiener space. To do this we first develop several rotation properties of the generalized Wiener integral associated with Gaussian processes. We then proceed to analyze the $L_2$ analytic Fourier-Feynman transforms associated with Gaussian processes. Our results show that these $L_2$ analytic Fourier--Feynman transforms are actually linear operator isomorphisms from a Hilbert space into itself. We finally investigate the algebraic structures of these classes of the transforms on Wiener space, and show that they indeed are group isomorphic.

math.PR↗

arXiv2019

A space of generalized Brownian motion path-valued continuous functions with application

In this paper, we introduce the paths space $\mathcal C_0^{\mathrm{gBm}}$ which is consists of generalized Brownian motion path-valued continuous functions on $[0,T]$. We next present several relevant examples of the paths space integral. We then discuss the concept of the analytic Feynman integration theory for functionals $F$ on the paths space $\mathcal C_0^{\mathrm{gBm}}$.

math.FA↗

arXiv2015

Analytic Fourier--Feynman transforms and convolution type operations associated with Gaussian processes on Wiener space

In this paper we introduce the concept of a convolution type operation of functionals on Wiener space. It contains several kinds of the concepts of convolution products on Wiener space, which have been studied by many authors. We then investigate fundamental relationships between generalized analytic Fourier--Feynman transforms and convolution type operations. Both of the generalized analytic Fourier--Feynman transform of the convolution type operation and the convolution type operation of the generalized analytic Fourier--Feynman transforms are represented as a product of the generalized analytic Fourier--Feynman transforms.

math.PR↗

arXiv2013

A generalized analytic Fourier-Feynman transform on the product function space $C_{a,b}^2[0,T]$ and related topics

In this paper we obtain various results involving the generalized analytic Fourier-Feynman transform and the first variation of functionals in a Fresnel type class defined on the product function space $C_{a,b}^2[0,T]$.

math.FA↗