
SIGMA 13 (2017), 085, 16 pages arXiv:1706.02391
https://doi.org/10.3842/SIGMA.2017.085
Contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications (OPSFA14)
The Inverse Spectral Problem for JacobiType Pencils
Sergey M. Zagorodnyuk
School of Mathematics and Computer Sciences, V.N. Karazin Kharkiv National University, Svobody Square 4, Kharkiv 61022, Ukraine
Received June 10, 2017, in final form October 24, 2017; Published online October 28, 2017
Abstract
In this paper we study the inverse spectral problem for Jacobitype pencils. By a Jacobitype pencil we mean the following pencil $J_5  \lambda J_3$, where $J_3$ is a Jacobi matrix and $J_5$ is a semiinfinite real symmetric fivediagonal 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.
Key words:
operator pencil; recurrence relation; orthogonal polynomials; spectral function.
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