New convolutions for the Hartley integral transform imbedded in the Banach algebras and convolution-type integral equations

This article presents two types of the new convolutions for the Hartley integral transform associated with the Hermite functions, gives rise to the identification of some commutative and non-commutative Banach algebras, and to the Young inequalities which, in a certain sense, can be seen as the exce...

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Main Authors: Tuan Nguyen Minh, Giang Bui Thi, Ha Quan Thai
Format: Article
Language:English
Published: De Gruyter 2025-02-01
Series:Demonstratio Mathematica
Subjects:
Online Access:https://doi.org/10.1515/dema-2024-0087
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author Tuan Nguyen Minh
Giang Bui Thi
Ha Quan Thai
author_facet Tuan Nguyen Minh
Giang Bui Thi
Ha Quan Thai
author_sort Tuan Nguyen Minh
collection DOAJ
description This article presents two types of the new convolutions for the Hartley integral transform associated with the Hermite functions, gives rise to the identification of some commutative and non-commutative Banach algebras, and to the Young inequalities which, in a certain sense, can be seen as the exceptional Young inequalities. Moreover, the solvability of a class of the integral equations is investigated, and their solutions in a series form can be obtained by using the constructed convolutions.
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spelling doaj-art-3f559743f00c44c5b30d8a934d8eb0242025-08-20T02:17:47ZengDe GruyterDemonstratio Mathematica2391-46612025-02-0158138138710.1515/dema-2024-0087New convolutions for the Hartley integral transform imbedded in the Banach algebras and convolution-type integral equationsTuan Nguyen Minh0Giang Bui Thi1Ha Quan Thai2Department of Mathematics, VNU University of Education, Vietnam National University, 144 Xuan Thuy, Cau Giay dist., Ha Noi, 10000, VietnamDepartment of Mathematics, Academy of Cryptography Technique, 141 Chien Thang rd., Thanh Tri dist., Ha Noi, 10000, VietnamDepartment of Computational and Applied Mathematics, VNU University of Natural Science, Vietnam National University, 334 Nguyen Trai, Thanh Xuan dist., Ha Noi, 10000, VietnamThis article presents two types of the new convolutions for the Hartley integral transform associated with the Hermite functions, gives rise to the identification of some commutative and non-commutative Banach algebras, and to the Young inequalities which, in a certain sense, can be seen as the exceptional Young inequalities. Moreover, the solvability of a class of the integral equations is investigated, and their solutions in a series form can be obtained by using the constructed convolutions.https://doi.org/10.1515/dema-2024-0087hartley’s integral transformgeneralized convolutionhermite’s functionswiener’s algebra42a3844a2044a3545e10
spellingShingle Tuan Nguyen Minh
Giang Bui Thi
Ha Quan Thai
New convolutions for the Hartley integral transform imbedded in the Banach algebras and convolution-type integral equations
Demonstratio Mathematica
hartley’s integral transform
generalized convolution
hermite’s functions
wiener’s algebra
42a38
44a20
44a35
45e10
title New convolutions for the Hartley integral transform imbedded in the Banach algebras and convolution-type integral equations
title_full New convolutions for the Hartley integral transform imbedded in the Banach algebras and convolution-type integral equations
title_fullStr New convolutions for the Hartley integral transform imbedded in the Banach algebras and convolution-type integral equations
title_full_unstemmed New convolutions for the Hartley integral transform imbedded in the Banach algebras and convolution-type integral equations
title_short New convolutions for the Hartley integral transform imbedded in the Banach algebras and convolution-type integral equations
title_sort new convolutions for the hartley integral transform imbedded in the banach algebras and convolution type integral equations
topic hartley’s integral transform
generalized convolution
hermite’s functions
wiener’s algebra
42a38
44a20
44a35
45e10
url https://doi.org/10.1515/dema-2024-0087
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