scholarly journals Correction: Young Sik, K. Partial Derivative Approach to the Integral Transform for the Function Space in the Banach Algebra. Entropy 2020, 22, 1047

Entropy ◽  
2020 ◽  
Vol 22 (12) ◽  
pp. 1369
Author(s):  
Kim Young Sik
Keyword(s):  
Banach Algebra ◽  
Function Space ◽  
Partial Derivative ◽  
Integral Transform

In the original article [...]

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.

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 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.

scholarly journals Conditional Fourier-Feynman Transforms with Drift on a Function Space

2019 ◽  
Vol 2019 ◽  
pp. 1-16
Author(s):  
Dong Hyun Cho ◽  
Suk Bong Park
Keyword(s):  
Banach Algebra ◽  
Function Space ◽  
Fourier Transforms ◽  
Convolution Product ◽  
Borel Measures ◽  
Conditional Expectations ◽  
Change Of Scale ◽  
Convolution Products ◽  
Complex Borel Measures ◽  
Generalized Cylinder

In this paper we derive change of scale formulas for conditional analytic Fourier-Feynman transforms and conditional convolution products of the functions which are the products of generalized cylinder functions and the functions in a Banach algebra which is the space of generalized Fourier transforms of the complex Borel measures on L2[0,T] using two simple formulas for conditional expectations with a drift on an analogue of Wiener space. Then we prove that the conditional transform of the conditional convolution product can be expressed by the product of the conditional transforms of each function. Finally we establish various changes of scale formulas for the conditional transforms and the conditional convolution products.

scholarly journals Some Applications of the Spectral Theory for the Integral Transform Involving the Spectral Representation

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Hyun Soo Chung ◽  
Seung Jun Chang
Keyword(s):  
Quantum Mechanics ◽  
Function Space ◽  
Spectral Theory ◽  
Spectral Representation ◽  
Integral Transform ◽  
Adjoint Operator ◽  
Function Spaces

In many previous papers, an integral transformℱγ,βwas just considered as a transform on appropriate function spaces. In this paper we deal with the integral transform as an operator on a function space. We then apply various operator theories toℱγ,β. Finally we give an application for the spectral representation of a self-adjoint operator which plays a key role in quantum mechanics.

scholarly journals Functional Space C(ω), C0(ω)

2012 ◽  
Vol 20 (1) ◽  
pp. 15-22
Author(s):  
Katuhiko Kanazashi ◽  
Hiroyuki Okazaki ◽  
Yasunari Shidama
Keyword(s):  
Topological Space ◽  
Banach Algebra ◽  
Function Space ◽  
Normed Space ◽  
Functional Space ◽  
Continuous Functions ◽  
Bounded Support ◽  
Compact Topological Space ◽  
Definition Of ◽  
Complex Valued

Functional Space C(ω), C0(ω) In this article, first we give a definition of a functional space which is constructed from all complex-valued continuous functions defined on a compact topological space. We prove that this functional space is a Banach algebra. Next, we give a definition of a function space which is constructed from all complex-valued continuous functions with bounded support. We also prove that this function space is a complex normed space.

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 Banach Algebra of Continuous Functionals and the Space of Real-Valued Continuous Functionals with Bounded Support

2010 ◽  
Vol 18 (1) ◽  
pp. 11-16 ◽  
Author(s):  
Katuhiko Kanazashi ◽  
Noboru Endou ◽  
Yasunari Shidama
Keyword(s):  
Topological Space ◽  
Banach Algebra ◽  
Function Space ◽  
Functional Space ◽  
Continuous Functions ◽  
Bounded Support ◽  
Compact Topological Space ◽  
Real Normed Space ◽  
Definition Of ◽  
Continuous Functionals

Banach Algebra of Continuous Functionals and the Space of Real-Valued Continuous Functionals with Bounded Support In this article, we give a definition of a functional space which is constructed from all continuous functions defined on a compact topological space. We prove that this functional space is a Banach algebra. Next, we give a definition of a function space which is constructed from all real-valued continuous functions with bounded support. We prove that this function space is a real normed space.

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

2020 ◽  
Author(s):  
Young Sik Kim
Keyword(s):  
Function Space ◽  
Partial Derivative ◽  
Feynman Integral ◽  
Wiener Integral ◽  
Analytic Feynman Integral ◽  
Change Of Scale

We investigate the behavior of the partial derivative approach to the change of scale formula and prove relationships among the analytic Wiener integral and the analytic Feynman integral of the partial derivative for the function space integral.

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