Basic Fundamental Formulas for Wiener Transforms Associated with a Pair of Operators on Hilbert Space

Segal introduce the Fourier–Wiener transform for the class of polynomial cylinder functions on Hilbert space, and Hida then develop this concept. Negrin define the extended Wiener transform with Hayker et al. In recent papers, Hayker et al. establish the existence, the composition formula, the inver...

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Autor principal:	Hyun Soo Chung
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Hilbert space convolution product first variation integration by parts formula translation theorem Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/23858e7822274af88cd0ecbe5e3f0afa
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spelling	oai:doaj.org-article:23858e7822274af88cd0ecbe5e3f0afa2021-11-11T18:17:12ZBasic Fundamental Formulas for Wiener Transforms Associated with a Pair of Operators on Hilbert Space10.3390/math92127382227-7390https://doaj.org/article/23858e7822274af88cd0ecbe5e3f0afa2021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2738https://doaj.org/toc/2227-7390Segal introduce the Fourier–Wiener transform for the class of polynomial cylinder functions on Hilbert space, and Hida then develop this concept. Negrin define the extended Wiener transform with Hayker et al. In recent papers, Hayker et al. establish the existence, the composition formula, the inversion formula, and the Parseval relation for the Wiener transform. But, they do not establish homomorphism properties for the Wiener transform. In this paper, the author establishes some basic fundamental formulas for the Wiener transform via some concepts and motivations introduced by Segal and used by Hayker et al. We then state the usefulness of basic fundamental formulas as some applications.Hyun Soo ChungMDPI AGarticleHilbert spaceconvolution productfirst variationintegration by parts formulatranslation theoremMathematicsQA1-939ENMathematics, Vol 9, Iss 2738, p 2738 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Hilbert space convolution product first variation integration by parts formula translation theorem Mathematics QA1-939
spellingShingle	Hilbert space convolution product first variation integration by parts formula translation theorem Mathematics QA1-939 Hyun Soo Chung Basic Fundamental Formulas for Wiener Transforms Associated with a Pair of Operators on Hilbert Space
description	Segal introduce the Fourier–Wiener transform for the class of polynomial cylinder functions on Hilbert space, and Hida then develop this concept. Negrin define the extended Wiener transform with Hayker et al. In recent papers, Hayker et al. establish the existence, the composition formula, the inversion formula, and the Parseval relation for the Wiener transform. But, they do not establish homomorphism properties for the Wiener transform. In this paper, the author establishes some basic fundamental formulas for the Wiener transform via some concepts and motivations introduced by Segal and used by Hayker et al. We then state the usefulness of basic fundamental formulas as some applications.
format	article
author	Hyun Soo Chung
author_facet	Hyun Soo Chung
author_sort	Hyun Soo Chung
title	Basic Fundamental Formulas for Wiener Transforms Associated with a Pair of Operators on Hilbert Space
title_short	Basic Fundamental Formulas for Wiener Transforms Associated with a Pair of Operators on Hilbert Space
title_full	Basic Fundamental Formulas for Wiener Transforms Associated with a Pair of Operators on Hilbert Space
title_fullStr	Basic Fundamental Formulas for Wiener Transforms Associated with a Pair of Operators on Hilbert Space
title_full_unstemmed	Basic Fundamental Formulas for Wiener Transforms Associated with a Pair of Operators on Hilbert Space
title_sort	basic fundamental formulas for wiener transforms associated with a pair of operators on hilbert space
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/23858e7822274af88cd0ecbe5e3f0afa
work_keys_str_mv	AT hyunsoochung basicfundamentalformulasforwienertransformsassociatedwithapairofoperatorsonhilbertspace
_version_	1718431870598774784

Basic Fundamental Formulas for Wiener Transforms Associated with a Pair of Operators on Hilbert Space

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