A new structure of an integral operator associated with trigonometric Dunkl settings
Abstract In this paper, we discuss a generalization to the Cherednik–Opdam integral operator to an abstract space of Boehmians. We introduce sets of Boehmians and establish delta sequences and certain class of convolution products. Then we prove that the extended Cherednik–Opdam integral operator is...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-07-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13662-021-03485-8 |
| _version_ | 1818652754784026624 |
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| author | Shrideh Khalaf Al-Omari Serkan Araci Mohammed Al-Smadi |
| author_facet | Shrideh Khalaf Al-Omari Serkan Araci Mohammed Al-Smadi |
| author_sort | Shrideh Khalaf Al-Omari |
| collection | DOAJ |
| description | Abstract In this paper, we discuss a generalization to the Cherednik–Opdam integral operator to an abstract space of Boehmians. We introduce sets of Boehmians and establish delta sequences and certain class of convolution products. Then we prove that the extended Cherednik–Opdam integral operator is linear, bijective and continuous with respect to the convergence of the generalized spaces of Boehmians. Moreover, we derive embeddings and discuss properties of the generalized theory. Moreover, we obtain an inversion formula and provide several results. |
| first_indexed | 2024-12-17T02:27:02Z |
| format | Article |
| id | doaj.art-00c5099847aa4384a1187c8717d30e38 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-17T02:27:02Z |
| publishDate | 2021-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-00c5099847aa4384a1187c8717d30e382022-12-21T22:07:04ZengSpringerOpenAdvances in Difference Equations1687-18472021-07-012021111210.1186/s13662-021-03485-8A new structure of an integral operator associated with trigonometric Dunkl settingsShrideh Khalaf Al-Omari0Serkan Araci1Mohammed Al-Smadi2Department of Physics and Basic Sciences, Faculty of Engineering Technology, Al-Balqa Applied UniversityDepartment of Economics, Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu UniversityDepartment of Applied Science, Ajloun College, Al-Balqa Applied UniversityAbstract In this paper, we discuss a generalization to the Cherednik–Opdam integral operator to an abstract space of Boehmians. We introduce sets of Boehmians and establish delta sequences and certain class of convolution products. Then we prove that the extended Cherednik–Opdam integral operator is linear, bijective and continuous with respect to the convergence of the generalized spaces of Boehmians. Moreover, we derive embeddings and discuss properties of the generalized theory. Moreover, we obtain an inversion formula and provide several results.https://doi.org/10.1186/s13662-021-03485-8Cherednik–Opdam integral operatorConvolution productPolynomialDifferential–difference operatorBoehmian |
| spellingShingle | Shrideh Khalaf Al-Omari Serkan Araci Mohammed Al-Smadi A new structure of an integral operator associated with trigonometric Dunkl settings Advances in Difference Equations Cherednik–Opdam integral operator Convolution product Polynomial Differential–difference operator Boehmian |
| title | A new structure of an integral operator associated with trigonometric Dunkl settings |
| title_full | A new structure of an integral operator associated with trigonometric Dunkl settings |
| title_fullStr | A new structure of an integral operator associated with trigonometric Dunkl settings |
| title_full_unstemmed | A new structure of an integral operator associated with trigonometric Dunkl settings |
| title_short | A new structure of an integral operator associated with trigonometric Dunkl settings |
| title_sort | new structure of an integral operator associated with trigonometric dunkl settings |
| topic | Cherednik–Opdam integral operator Convolution product Polynomial Differential–difference operator Boehmian |
| url | https://doi.org/10.1186/s13662-021-03485-8 |
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