The Inverse Spectral Problem for Jacobi-Type Pencils

Symmetry Integrability and Geometry-Methods and Applications

article

Sergey M. Zagorodnyuk¹ 

[1] School of Mathematics and Computer Sciences, V.N. Karazin Kharkiv National University

关键词: operator pencil;    recurrence relation;    orthogonal polynomials;    spectral function;   

DOI  :  10.3842/SIGMA.2017.085

来源: National Academy of Science of Ukraine

【 摘 要 】

In this paper we study the inverse spectral problem for Jacobi-type pencils. By a Jacobi-type pencil we mean the following pencil $J_5 - \lambda J_3$, 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. In the case of a special perturbation of orthogonal polynomials on a finite interval the corresponding spectral function takes an explicit form.

【 授权许可】

Unknown