Convolution and analytic Fourier-Feynman transforms over paths in abstract Wiener space

K. S. Chang; B. S. Kim; T. S. Song; I. Yoo

doi:10.1080/10652460213523

Convolution and analytic Fourier-Feynman transforms over paths in abstract Wiener space

K. S. Chang
, B. S. Kim
, T. S. Song
, I. Yoo

School of Natural Sciences

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

In this paper, we define an L_p analytic Fourier-Feynman transform on C₀(B), the space of abstract Wiener space valued continuous functions on [0, T]. We establish existence theorems and inverse transform theorems of this transform for some classes of cylinder type functions on C₀(B) having the form F(x) =f((h₁, x(s₁))̃, ..., (h_m, x(S_n))̃). Moreover we present various relationships involving convolution and the transforms.

Original language	English
Pages (from-to)	345-362
Number of pages	18
Journal	Integral Transforms and Special Functions
Volume	13
Issue number	4
DOIs	https://doi.org/10.1080/10652460213523
State	Published - Aug 2002

Keywords

Abstract Wiener space
Analytic Feynman integral
Convolution
Fourier-Feynman transform

Access to Document

10.1080/10652460213523

Cite this

@article{cf71207ca5484e3bb674a2d796af8535,

title = "Convolution and analytic Fourier-Feynman transforms over paths in abstract Wiener space",

abstract = "In this paper, we define an Lp analytic Fourier-Feynman transform on C0(B), the space of abstract Wiener space valued continuous functions on [0, T]. We establish existence theorems and inverse transform theorems of this transform for some classes of cylinder type functions on C0(B) having the form F(x) =f((h1, x(s1){\~)}, ..., (hm, x(Sn){\~)}). Moreover we present various relationships involving convolution and the transforms.",

keywords = "Abstract Wiener space, Analytic Feynman integral, Convolution, Fourier-Feynman transform",

author = "Chang, \{K. S.\} and Kim, \{B. S.\} and Song, \{T. S.\} and I. Yoo",

year = "2002",

month = aug,

doi = "10.1080/10652460213523",

language = "English",

volume = "13",

pages = "345--362",

journal = "Integral Transforms and Special Functions",

issn = "1065-2469",

number = "4",

}

TY - JOUR

T1 - Convolution and analytic Fourier-Feynman transforms over paths in abstract Wiener space

AU - Chang, K. S.

AU - Kim, B. S.

AU - Song, T. S.

AU - Yoo, I.

PY - 2002/8

Y1 - 2002/8

N2 - In this paper, we define an Lp analytic Fourier-Feynman transform on C0(B), the space of abstract Wiener space valued continuous functions on [0, T]. We establish existence theorems and inverse transform theorems of this transform for some classes of cylinder type functions on C0(B) having the form F(x) =f((h1, x(s1))̃, ..., (hm, x(Sn))̃). Moreover we present various relationships involving convolution and the transforms.

AB - In this paper, we define an Lp analytic Fourier-Feynman transform on C0(B), the space of abstract Wiener space valued continuous functions on [0, T]. We establish existence theorems and inverse transform theorems of this transform for some classes of cylinder type functions on C0(B) having the form F(x) =f((h1, x(s1))̃, ..., (hm, x(Sn))̃). Moreover we present various relationships involving convolution and the transforms.

KW - Abstract Wiener space

KW - Analytic Feynman integral

KW - Convolution

KW - Fourier-Feynman transform

UR - https://www.scopus.com/pages/publications/0036023571

U2 - 10.1080/10652460213523

DO - 10.1080/10652460213523

M3 - Article

AN - SCOPUS:0036023571

SN - 1065-2469

VL - 13

SP - 345

EP - 362

JO - Integral Transforms and Special Functions

JF - Integral Transforms and Special Functions

IS - 4

ER -

Convolution and analytic Fourier-Feynman transforms over paths in abstract Wiener space

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this