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...
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| Дата: | 2016 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2016
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/1913 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | 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. |
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