scholarly journals Generalized convolution product for an integral transform on a Wiener space

2017 ◽  
Vol 41 ◽  
pp. 940-955 ◽  
Author(s):  
Byoung Soo KIM ◽  
Il YOO
Keyword(s):  
Integral Transform ◽  
Wiener Space ◽  
Convolution Product ◽  
Generalized Convolution

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 integral transforms with the translation operator on function space

Filomat ◽  
2019 ◽  
Vol 33 (3) ◽  
pp. 869-880
Author(s):  
Seung Chang ◽  
Jae Choi ◽  
Hyun Chung
Keyword(s):  
Integral Transform ◽  
Integral Transforms ◽  
Translation Operator ◽  
Convolution Product ◽  
Generalized Convolution ◽  
Brownian Motion Process ◽  
Motion Process ◽  
Generalized Brownian Motion Process ◽  
Nonzero Mean ◽  
Mean Function

Main goal of this paper is to establish various basic formulas for the generalized integral transform involving the generalized convolution product. In order to establish these formulas, we use the translation operator which was introduced in [9]. It was not easy to establish basic formulas for the generalized integral transforms because the generalized Brownian motion process used in this paper has the nonzero mean function. In this paper, we can easily establish various basic formulas for the generalized integral transform involving the generalized convolution product via the translation operator.

scholarly journals Some Relationships for the Generalized Integral Transform on Function Space

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2246
Author(s):  
Hyun Chung
Keyword(s):  
Gaussian Process ◽  
Function Space ◽  
Integral Transform ◽  
Linear Operators ◽  
Convolution Product ◽  
Generalized Convolution ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
First Variation

In this paper, we recall a more generalized integral transform, a generalized convolution product and a generalized first variation on function space. The Gaussian process and the bounded linear operators on function space are used to define them. We then establish the existence and various relationships between the generalized integral transform and the generalized convolution product. Furthermore, we obtain some relationships between the generalized integral transform and the generalized first variation with the generalized Cameron–Storvick theorem. Finally, some applications are demonstrated as examples.

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.

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 Integral transforms, convolution products, and first variations

2004 ◽  
Vol 2004 (11) ◽  
pp. 579-598 ◽  
Author(s):  
Bong Jin Kim ◽  
Byoung Soo Kim ◽  
David Skoug
Keyword(s):  
Integral Transform ◽  
Integral Transforms ◽  
Continuous Functions ◽  
Convolution Product ◽  
First Variation ◽  
Alpha Beta ◽  
Convolution Products ◽  
The First Variation ◽  
Complex Valued

We establish the various relationships that exist among the integral transformℱα,βF, the convolution product(F∗G)α, and the first variationδFfor a class of functionals defined onK[0,T], the space of complex-valued continuous functions on[0,T]which vanish at zero.

scholarly journals Change of Scale Formulas for Wiener Integrals Related to Fourier-Feynman Transform and Convolution

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Bong Jin Kim ◽  
Byoung Soo Kim ◽  
Il Yoo
Keyword(s):  
Banach Algebra ◽  
Wiener Space ◽  
Convolution Product ◽  
Abstract Wiener Space ◽  
Change Of Scale ◽  
Generalized Fresnel Class

Cameron and Storvick discovered change of scale formulas for Wiener integrals of functionals in Banach algebraSon classical Wiener space. Yoo and Skoug extended these results for functionals in the Fresnel classF(B)and in a generalized Fresnel classFA1,A2on abstract Wiener space. We express Fourier-Feynman transform and convolution product of functionals inSas limits of Wiener integrals. Moreover we obtain change of scale formulas for Wiener integrals related to Fourier-Feynman transform and convolution product of these functionals.

scholarly journals Generalized Integral Transforms via the Series Expressions

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 539 ◽  
Author(s):  
Hyun Soo Chung
Keyword(s):  
Integral Transform ◽  
Integral Transforms ◽  
Wiener Space ◽  
New Method ◽  
Variable Formula ◽  
Change Of Variable ◽  
Conventional Methods

From the change of variable formula on the Wiener space, we calculate various integral transforms for functionals on the Wiener space. However, not all functionals can be obtained by using this formula. In the process of calculating the integral transform introduced by Lee, this formula is also used, but it is also not possible to calculate for all the functionals. In this paper, we define a generalized integral transform. We then introduce a new method to evaluate the generalized integral transform for functionals using series expressions. Our method can be used to evaluate various functionals that cannot be calculated by conventional methods.

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