Orthogonal polynomials related to some Jacobi-type pencils

• Date: 2016
• Main Authors: Zagorodnyuk, S. M., Загороднюк, С. М.
• Format: Article
• Language: Russian
• Published: Institute of Mathematics, NAS of Ukraine 2016
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1913
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...