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This article is cited in 4 scientific papers (total in 4 papers)
The Inverse Spectral Problem for Jacobi-Type Pencils
Sergey M. Zagorodnyuk School of Mathematics and Computer Sciences, V.N. Karazin Kharkiv National University, Svobody Square 4, Kharkiv 61022, Ukraine
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.
Keywords:
operator pencil; recurrence relation; orthogonal polynomials; spectral function.
Received: June 10, 2017; in final form October 24, 2017; Published online October 28, 2017
Citation:
Sergey M. Zagorodnyuk, “The Inverse Spectral Problem for Jacobi-Type Pencils”, SIGMA, 13 (2017), 085, 16 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1285 https://www.mathnet.ru/eng/sigma/v13/p85
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Abstract page: | 144 | Full-text PDF : | 28 | References: | 23 |
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