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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| Format: | Article |
| Language: | English |
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De Gruyter
2025-02-01
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| Series: | Demonstratio Mathematica |
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| 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. |
| format | Article |
| id | doaj-art-3f559743f00c44c5b30d8a934d8eb024 |
| institution | OA Journals |
| issn | 2391-4661 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| 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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