The Inverse Spectral Problem for Jacobi-Type Pencils
Sergey M. Zagorodnyuk · Symmetry Integrability and Geometry Methods and Applications · 2017
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 -λJ 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.