HAHN'S PROBLEM WITH RESPECT TO SOME PERTURBATIONS OF THE RAISING OPERATOR \(X-c\)
In this paper, we study the Hahn's problem with respect to some raising operators perturbed of the operator \(X-c\), where \(c\) is an arbitrary complex number. More precisely, the two following characterizations hold: up to a normalization, the \(q\)-Hermite (resp. Charlier) polynomial is the...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin.
2020-12-01
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| Series: | Ural Mathematical Journal |
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| Online Access: | https://umjuran.ru/index.php/umj/article/view/259 |
| _version_ | 1818393525043068928 |
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| author | Baghdadi Aloui Jihad Souissi |
| author_facet | Baghdadi Aloui Jihad Souissi |
| author_sort | Baghdadi Aloui |
| collection | DOAJ |
| description | In this paper, we study the Hahn's problem with respect to some raising operators perturbed of the operator \(X-c\), where \(c\) is an arbitrary complex number. More precisely, the two following characterizations hold: up to a normalization, the \(q\)-Hermite (resp. Charlier) polynomial is the only \(H_{\alpha,q}\)-classical (resp. \(\mathcal{S}_{\lambda}\)-classical) orthogonal polynomial, where \(H_{\alpha, q}:=X+\alpha H_q\) and \(\mathcal{S}_{\lambda}:=(X+1)-\lambda\tau_{-1}.\) |
| first_indexed | 2024-12-14T05:46:41Z |
| format | Article |
| id | doaj.art-994577760f944edd896392369caf8007 |
| institution | Directory Open Access Journal |
| issn | 2414-3952 |
| language | English |
| last_indexed | 2024-12-14T05:46:41Z |
| publishDate | 2020-12-01 |
| publisher | Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin. |
| record_format | Article |
| series | Ural Mathematical Journal |
| spelling | doaj.art-994577760f944edd896392369caf80072022-12-21T23:14:51ZengKrasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin.Ural Mathematical Journal2414-39522020-12-016210.15826/umj.2020.2.002110HAHN'S PROBLEM WITH RESPECT TO SOME PERTURBATIONS OF THE RAISING OPERATOR \(X-c\)Baghdadi Aloui0Jihad Souissi1University of Gabes, Higher Institute of Industrial Systems of Gabes, Street Salah Eddine Elayoubi, 6033 GabesUniversity of Gabes, Faculty of Sciences of Gabes, Street Erriadh 6072 GabesIn this paper, we study the Hahn's problem with respect to some raising operators perturbed of the operator \(X-c\), where \(c\) is an arbitrary complex number. More precisely, the two following characterizations hold: up to a normalization, the \(q\)-Hermite (resp. Charlier) polynomial is the only \(H_{\alpha,q}\)-classical (resp. \(\mathcal{S}_{\lambda}\)-classical) orthogonal polynomial, where \(H_{\alpha, q}:=X+\alpha H_q\) and \(\mathcal{S}_{\lambda}:=(X+1)-\lambda\tau_{-1}.\)https://umjuran.ru/index.php/umj/article/view/259orthogonal polynomials, linear functional, \(\mathcal{o}\)-classical polynomials, raising operators, \(q\)-hermite polynomials, charlier polynomials |
| spellingShingle | Baghdadi Aloui Jihad Souissi HAHN'S PROBLEM WITH RESPECT TO SOME PERTURBATIONS OF THE RAISING OPERATOR \(X-c\) Ural Mathematical Journal orthogonal polynomials, linear functional, \(\mathcal{o}\)-classical polynomials, raising operators, \(q\)-hermite polynomials, charlier polynomials |
| title | HAHN'S PROBLEM WITH RESPECT TO SOME PERTURBATIONS OF THE RAISING OPERATOR \(X-c\) |
| title_full | HAHN'S PROBLEM WITH RESPECT TO SOME PERTURBATIONS OF THE RAISING OPERATOR \(X-c\) |
| title_fullStr | HAHN'S PROBLEM WITH RESPECT TO SOME PERTURBATIONS OF THE RAISING OPERATOR \(X-c\) |
| title_full_unstemmed | HAHN'S PROBLEM WITH RESPECT TO SOME PERTURBATIONS OF THE RAISING OPERATOR \(X-c\) |
| title_short | HAHN'S PROBLEM WITH RESPECT TO SOME PERTURBATIONS OF THE RAISING OPERATOR \(X-c\) |
| title_sort | hahn s problem with respect to some perturbations of the raising operator x c |
| topic | orthogonal polynomials, linear functional, \(\mathcal{o}\)-classical polynomials, raising operators, \(q\)-hermite polynomials, charlier polynomials |
| url | https://umjuran.ru/index.php/umj/article/view/259 |
| work_keys_str_mv | AT baghdadialoui hahnsproblemwithrespecttosomeperturbationsoftheraisingoperatorxc AT jihadsouissi hahnsproblemwithrespecttosomeperturbationsoftheraisingoperatorxc |