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arXiv · 1706.02391

The Inverse Spectral Problem for Jacobi-Type Pencils

Sergey M. Zagorodnyuk
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Abstract

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.

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Sergey M. Zagorodnyuk. 2017-06-07. The Inverse Spectral Problem for Jacobi-Type Pencils. https://doi.org/10.3842/sigma.2017.085

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