Ladder operators and a second--order difference equation for general discrete Sobolev orthogonal polynomials
| Autor: | Filipuk, Galina, Mañas-Mañas, Juan F., Moreno-Balcázar, Juan J. |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Journal of Difference Equations and Applications (2022) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1080/10236198.2022.2103412 |
| Popis: | We consider a general discrete Sobolev inner product involving the Hahn difference operator, so this includes the well--known difference operators $\mathscr{D}_{q}$ and $\Delta$ and, as a limit case, the derivative operator. The objective is twofold. On the one hand, we construct the ladder operators for the corresponding nonstandard orthogonal polynomials and we obtain the second--order difference equation satisfied by these polynomials. On the other hand, we generalise some related results appeared in the literature as we are working in a more general framework. Moreover, we will show that all the functions involved in these constructions can be computed explicitly. Comment: Preprint of the version published in Journal of Difference Equations and Applications with the title "Second--order difference equation for Sobolev--type orthogonal polynomials: Part I: theoretical results" |
| Databáze: | arXiv |
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