A NEW CHARACTERIZATION OF SYMMETRIC DUNKL AND Q-DUNKL-CLASSICAL ORTHOGONAL POLYNOMIALS
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
A NEW CHARACTERIZATION OF SYMMETRIC DUNKL AND Q-DUNKL-CLASSICAL ORTHOGONAL POLYNOMIALS
|
|
| Автор |
Habbachi, Ya.
|
|
| Тематика |
RTHOGONAL POLYNOMIALS
DUNKL OPERATOR Q-DUNKL OPERATOR |
|
| Описание |
In this paper, we consider the following L-difference equation Φ(x)LPn+1(x)=(ξnx+ϑn)Pn+1(x)+λnPn(x),n≥0, where Φ is a monic polynomial (even), degΦ≤2, ξn,ϑn,λn,n≥0, are complex numbers and L is either the Dunkl operator Tμ or the the q-Dunkl operator T(θ,q). We show that if L=Tμ, then the only symmetric orthogonal polynomials satisfying the previous equation are, up a dilation, the generalized Hermite polynomials and the generalized Gegenbauer polynomials and if L=T(θ,q), then the q2-analogue of generalized Hermite and the q2-analogue of generalized Gegenbauer polynomials are, up a dilation, the only orthogonal polynomials sequences satisfying the L-difference equation.
|
|
| Дата |
2024-02-14T05:20:30Z
2024-02-14T05:20:30Z 2023 |
|
| Тип |
Article
Journal article (info:eu-repo/semantics/article) Published version (info:eu-repo/semantics/publishedVersion) |
|
| Идентификатор |
Habbachi Ya. A NEW CHARACTERIZATION OF SYMMETRIC DUNKL AND Q-DUNKL-CLASSICAL ORTHOGONAL POLYNOMIALS / Ya. Habbachi. — Text : electronic // Ural Mathematical Journal. — 2023. — Volume 9. — № 2. — P. 109-120.
2414-3952 https://umjuran.ru/index.php/umj/article/view/485 http://elar.urfu.ru/handle/10995/129421 59690657 10.15826/umj.2023.2.009 |
|
| Язык |
en
|
|
| Связанные ресурсы |
Ural Mathematical Journal. 2023. Volume 9. № 2
|
|
| Права |
Creative Commons Attribution License
https://creativecommons.org/licenses/by/4.0/ |
|
| Формат |
application/pdf
|
|