تقرير
Bispectrality and biorthogonality of the rational functions of $q$-Hahn type
| العنوان: | Bispectrality and biorthogonality of the rational functions of $q$-Hahn type |
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| المؤلفون: | Bussière, Ismaël, Gaboriaud, Julien, Vinet, Luc, Zhedanov, Alexei |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematics - Classical Analysis and ODEs, Mathematical Physics, 33D45, 42C05, 47B36 |
| الوصف: | We introduce families of rational functions that are biorthogonal with respect to the $q$-hypergeometric distribution. A triplet of $q$-difference operators $X$, $Y$, $Z$ is shown to play a role analogous to the pair of bispectral operators of orthogonal polynomials. The recurrence relation and difference equation take the form of generalized eigenvalue problems involving the three operators. The algebra generated by $X$, $Y$, $Z$ is akin to the algebras of Askey--Wilson type in the case of orthogonal polynomials. The actions of these operators in three different basis are presented. Connections with Wilson's ${}_{10}\phi_9$ biorthogonal rational functions are also discussed. Comment: 19 pages, updated version to match the one accepted for publication |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1016/j.jmaa.2022.126443 |
| URL الوصول: | http://arxiv.org/abs/2202.05925 |
| رقم الأكسشن: | edsarx.2202.05925 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1016/j.jmaa.2022.126443 |
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