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 Relationships of convolution products, generalized transforms, and the first variation on function space

2002 ◽  
Vol 29 (10) ◽  
pp. 591-608 ◽  
Author(s):  
Seung Jun Chang ◽  
Jae Gil Choi
Keyword(s):  
Brownian Motion ◽  
Banach Algebra ◽  
Function Space ◽  
Standard Wiener Process ◽  
Convolution Product ◽  
Brownian Motion Process ◽  
First Variation ◽  
Motion Process ◽  
Generalized Brownian Motion Process ◽  
The First Variation

We use a generalized Brownian motion process to define the generalized Fourier-Feynman transform, the convolution product, and the first variation. We then examine the various relationships that exist among the first variation, the generalized Fourier-Feynman transform, and the convolution product for functionals on function space that belong to a Banach algebraS(Lab[0,T]). These results subsume similar known results obtained by Park, Skoug, and Storvick (1998) for the standard Wiener process.

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 Conditional generalized analytic Feynman integrals and a generalized integral equation

2000 ◽  
Vol 23 (11) ◽  
pp. 759-776 ◽  
Author(s):  
Seung Jun Chang ◽  
Soon Ja Kang ◽  
David Skoug
Keyword(s):  
Integral Equation ◽  
Brownian Motion ◽  
Feynman Integral ◽  
Brownian Motion Process ◽  
Feynman Integrals ◽  
Motion Process ◽  
Generalized Brownian Motion Process

We use a generalized Brownian motion process to define a generalized Feynman integral and a conditional generalized Feynman integral. We then establish the existence of these integrals for various functionals. Finally we use the conditional generalized Feynman integral to derive a Schrödinger integral equation.

scholarly journals Sequential Generalized Transforms on Function Space

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Jae Gil Choi ◽  
Hyun Soo Chung ◽  
Seung Jun Chang
Keyword(s):  
Brownian Motion ◽  
Banach Algebra ◽  
Function Space ◽  
The Other ◽  
Brownian Motion Process ◽  
Inverse Transform ◽  
Motion Process ◽  
Generalized Brownian Motion Process

We define two sequential transforms on a function spaceCa,b[0,T]induced by generalized Brownian motion process. We then establish the existence of the sequential transforms for functionals in a Banach algebra of functionals onCa,b[0,T]. We also establish that any one of these transforms acts like an inverse transform of the other transform. Finally, we give some remarks about certain relations between our sequential transforms and other well-known transforms onCa,b[0,T].

scholarly journals Conditional integral transforms with related topics on function space

Filomat ◽  
2012 ◽  
Vol 26 (6) ◽  
pp. 1151-1162 ◽  
Author(s):  
Hyun Chung ◽  
Jae Choi ◽  
Seung Chang
Keyword(s):  
Function Space ◽  
Integral Transform ◽  
Integral Transforms ◽  
Convolution Product ◽  
First Variation ◽  
Convolution Products ◽  
The First Variation

In this paper we study the conditional integral transform, the conditional convolution product and the first variation of functionals on function space. For our research, we modify the class S? of functionals introduced in [7]. We then give the existences of the conditional integral transform, the conditional convolution product and the first variation for functionals in S?. Finally, we give various relationships and formulas among conditional integral transforms, conditional convolution products and first variations of functionals in S?.

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 Generalized analytic Fourier-Feynman transforms with respect to Gaussian processes on function space

Filomat ◽  
2016 ◽  
Vol 30 (6) ◽  
pp. 1615-1624
Author(s):  
Seung Chang ◽  
Hyun Chung ◽  
Ae Ko ◽  
Jae Choi
Keyword(s):  
Brownian Motion ◽  
Function Space ◽  
Gaussian Processes ◽  
Brownian Motion Process ◽  
Motion Process ◽  
Generalized Brownian Motion Process

In this article, we introduce a generalized analytic Fourier-Feynman transform and a multiple generalized analytic Fourier-Feynman transform with respect to Gaussian processes on the function space Ca,b[0,T] induced by generalized Brownian motion process. We derive a rotation formula for our multiple generalized analytic Fourier-Feynman transform.

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