scholarly journals A Rotation on Wiener Space with Applications

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Jae Gil Choi ◽  
Seung Jun Chang
Keyword(s):  
Feynman Integral ◽  
Wiener Measure ◽  
Wiener Space ◽  
Fundamental Result ◽  
Convolution Product ◽  
Generalized Convolution ◽  
Analytic Feynman Integral ◽  
Generalized Analytic Feynman Integral ◽  
Wiener Spaces

We first investigate a rotation property of Wiener measure on the product of Wiener spaces. Next, using the concept of the generalized analytic Feynman integral, we define a generalized Fourier-Feynman transform and a generalized convolution product for functionals on Wiener space. We then proceed to establish a fundamental result involving the generalized transform and the generalized convolution product.

A MULTIPLE GENERALIZED FOURIER–FEYNMAN TRANSFORM VIA A ROTATION ON WIENER SPACE

2012 ◽  
Vol 23 (07) ◽  
pp. 1250068 ◽  
Author(s):  
JAE GIL CHOI ◽  
DAVID SKOUG ◽  
SEUNG JUN CHANG
Keyword(s):  
Wiener Measure ◽  
Wiener Space ◽  
Convolution Product ◽  
Generalized Convolution ◽  
Algebraic Properties

In this paper we use a rotation property of Wiener measure to define a very general multiple Fourier–Feynman transform on Wiener space. We then proceed to establish its many algebraic properties as well as to establish several relationships between this generalized multiple transform and the corresponding generalized convolution product.

scholarly journals Generalized transforms and convolutions

1997 ◽  
Vol 20 (1) ◽  
pp. 19-32 ◽  
Author(s):  
Timothy Huffman ◽  
Chull Park ◽  
David Skoug
Keyword(s):  
Feynman Integral ◽  
Wiener Space ◽  
Convolution Product ◽  
Generalized Convolution

In this paper, using the concept of a generalized Feynman integral, we define a generalized Fourier-Feynman transform and a generalized convolution product. Then for two classes of functionals on Wiener space we obtain several results involving and relating these generalized transforms and convolutions. In particular we show that the generalized transform of the convolution product is a product of transforms. In addition we establish a Parseval's identity for functionals in each of these classes.

scholarly journals Analytic Feynman Integral and a Change of Scale Formula for Wiener Integrals of an Unbounded Cylinder Function

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Kim Young Sik
Keyword(s):  
Feynman Integral ◽  
Wiener Space ◽  
Wiener Integral ◽  
Unbounded Function ◽  
Cylinder Function ◽  
Analytic Feynman Integral ◽  
Change Of Scale ◽  
Unbounded Cylinder

We investigate the behavior of the unbounded cylinder function F x = ∫ 0 T α 1 t d x t 2 k ⋅ ∫ 0 T α 2 t d x t 2 k ⋅ ⋯ ⋅ ∫ 0 T α n t d x t 2 k ,   k = 1,2 , … whose analytic Wiener integral and analytic Feynman integral exist, we prove some relationships among the analytic Wiener integral, the analytic Feynman integral, and the Wiener integral, and we prove a change of scale formula for the Wiener integral about the unbounded function on the Wiener space C 0 0 , T .

scholarly journals A change of scale formula for Wiener integrals of cylinder functions on abstract Wiener space

1998 ◽  
Vol 21 (1) ◽  
pp. 73-78 ◽  
Author(s):  
Young Sik Kim
Keyword(s):  
Feynman Integral ◽  
Wiener Space ◽  
Abstract Wiener Space ◽  
Wiener Integral ◽  
Feynman Integrals ◽  
Analytic Feynman Integral ◽  
Change Of Scale ◽  
The Relationship

The purpose of this paper is to establish the existence of analytic Wiener and Feynman integrals for a class of certain cylinder functions which is of the form:F(x)=f((h1,x)∼,⋯,(hn,x)∼),    x∈B,on the abstract Wiener space, and to establish the relationship between the Wiener integral and the analytic Feynman integral for such cylinder functions on the abstract Wiener space. We then establish a change of scale formula for Wiener integrals of such cylinder functions on the abstract Wiener space.

scholarly journals A change of scale formula for Wiener integrals of cylinder functions on the abstract Wiener space II

2001 ◽  
Vol 25 (4) ◽  
pp. 231-237 ◽  
Author(s):  
Young Sik Kim
Keyword(s):  
Fourier Transform ◽  
Borel Measure ◽  
Feynman Integral ◽  
Wiener Space ◽  
Abstract Wiener Space ◽  
Analytic Feynman Integral ◽  
Change Of Scale ◽  
The Fourier Transform ◽  
Complex Valued

We show that for certain bounded cylinder functions of the formF(x)=μˆ((h1,x)∼,...,(hn,x)∼),x∈Bwhereμˆ:ℝn→ℂis the Fourier-transform of the complex-valued Borel measureμonℬ(ℝn), the Borelσ-algebra ofℝnwith‖μ‖<∞, the analytic Feynman integral ofFexists, although the analytic Feynman integral,limz→−iqIaw(F;z)=limz→−iq(z/2π)n/2∫ℝnf(u→)exp{−(z/2)|u→|2}du→, do not always exist for bounded cylinder functionsF(x)=f((h1,x)∼,...,(hn,x)∼),x∈B. We prove a change of scale formula for Wiener integrals ofFon the abstract Wiener space.

Sign in / Sign up

Export Citation Format

Share Document