Orthogonal polynomials related to some Jacobi-type pencils
We study a generalization of the class of orthonormal polynomials on the real axis. These polynomials satisfy the following relation: $(J_5 \lambda J_3)\vec{p}(\lambda) = 0$, where $J_3$ is a Jacobi matrix and $J_5$ is a semi-infinite real symmetric five-diagonal matrix with positive numbers on the...
Gespeichert in:
| Datum: | 2016 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2016
|
| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/1913 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Institution
Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | We study a generalization of the class of orthonormal polynomials on the real axis. These polynomials satisfy the following
relation: $(J_5 \lambda J_3)\vec{p}(\lambda) = 0$, where $J_3$ is a Jacobi matrix and $J_5$ is a semi-infinite real symmetric five-diagonal matrix with positive numbers on the second subdiagonal, $\vec{p}(\lambda) = (p_0(\lambda ), p_1(\lambda ), p_2(\lambda ),...)^T$, the superscript $T$ denotes the operation of transposition with the initial conditions $p_0(\lambda ) = 1,\; p_1(\lambda) = \alpha \lambda + \beta,\; \alpha > 0, \beta \in R$. Certain orthonormality
conditions for the polynomials $\{ pn(\lambda )\}^{\infty}_n = 0$ are obtained. An explicit example of these polynomials is constructed. |
|---|