Geodesic
The Inverse Spectral Problem for Jacobi-Type Pencils
Symmetry, integrability and geometry: methods and applications, Tome 13 (2017) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: operator pencil; recurrence relation; orthogonal polynomials; spectral function. 
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     author = {Sergey M. Zagorodnyuk},
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Sergey M. Zagorodnyuk. The Inverse Spectral Problem for Jacobi-Type Pencils. Symmetry, integrability and geometry: methods and applications, Tome 13 (2017). http://geodesic.mathdoc.fr/item/SIGMA_2017_13_a84/

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