scholarly journals Partial Derivative Approach to the Integral Transform for the Function Space in the Banach Algebra

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 1047 ◽  
Author(s):  
Kim Young Sik
Keyword(s):  
Banach Algebra ◽  
Function Space ◽  
Partial Derivative ◽  
Integral Transform ◽  
First Variation ◽  
The First Variation

We investigate some relationships among the integral transform, the function space integral and the first variation of the partial derivative approach in the Banach algebra defined on the function space. We prove that the function space integral and the integral transform of the partial derivative in some Banach algebra can be expanded as the limit of a sequence of function space integrals.

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 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 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.

A SPHERICAL VERSION OF THE KOWALSKI–SŁODKOWSKI THEOREM AND ITS APPLICATIONS

2020 ◽  
pp. 1-26
Author(s):  
SHIHO OI
Keyword(s):  
Banach Algebra ◽  
Function Space ◽  
Affirmative Answer ◽  
List Type ◽  
Private Communication ◽  
Type Number ◽  
Uniform Algebras ◽  
Surjective Isometry ◽  
Complex Linear ◽  
Local Map

Abstract Li et al. [‘Weak 2-local isometries on uniform algebras and Lipschitz algebras’, Publ. Mat.63 (2019), 241–264] generalized the Kowalski–Słodkowski theorem by establishing the following spherical variant: let A be a unital complex Banach algebra and let $\Delta : A \to \mathbb {C}$ be a mapping satisfying the following properties: (a) $\Delta $ is 1-homogeneous (that is, $\Delta (\lambda x)=\lambda \Delta (x)$ for all $x \in A$ , $\lambda \in \mathbb C$ ); (b) $\Delta (x)-\Delta (y) \in \mathbb {T}\sigma (x-y), \quad x,y \in A$ . Then $\Delta $ is linear and there exists $\lambda _{0} \in \mathbb {T}$ such that $\lambda _{0}\Delta $ is multiplicative. In this note we prove that if (a) is relaxed to $\Delta (0)=0$ , then $\Delta $ is complex-linear or conjugate-linear and $\overline {\Delta (\mathbf {1})}\Delta $ is multiplicative. We extend the Kowalski–Słodkowski theorem as a conclusion. As a corollary, we prove that every 2-local map in the set of all surjective isometries (without assuming linearity) on a certain function space is in fact a surjective isometry. This gives an affirmative answer to a problem on 2-local isometries posed by Molnár [‘On 2-local *-automorphisms and 2-local isometries of B(H)', J. Math. Anal. Appl.479(1) (2019), 569–580] and also in a private communication between Molnár and O. Hatori, 2018.

scholarly journals Existence Results for the Conformal Dirac–Einstein System

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Chiara Guidi ◽  
Ali Maalaoui ◽  
Vittorio Martino
Keyword(s):  
Perturbation Methods ◽  
Existence Of Solutions ◽  
Coupled System ◽  
Existence Results ◽  
First Variation ◽  
The First Variation

AbstractWe consider the coupled system given by the first variation of the conformal Dirac–Einstein functional. We will show existence of solutions by means of perturbation methods.

scholarly journals A Partial Derivative Approach to the Change of Scale Formula for the Function Space Integral

Entropy ◽  
2020 ◽  
Vol 23 (1) ◽  
pp. 26
Author(s):  
Young Sik Kim
Keyword(s):  
Fourier Transform ◽  
Function Space ◽  
Partial Derivative ◽  
Directional Derivative ◽  
Feynman Integral ◽  
Wiener Integral ◽  
Vector Calculus ◽  
Change Of Scale

We investigate the partial derivative approach to the change of scale formula for the functon space integral and we investigate the vector calculus approach to the directional derivative on the function space and prove relationships among the Wiener integral and the Feynman integral about the directional derivative of a Fourier transform.

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