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The Inverse Spectral Problem for Jacobi-Type Pencils
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2017, том 13
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The Inverse Spectral Problem for Jacobi-Type Pencils
Інший ID:
2010 Mathematics Subject Classification: 42C05; 47B36
DOI:10.3842/SIGMA.2017.085
DOI:10.3842/SIGMA.2017.085
Посилання:
The Inverse Spectral Problem for Jacobi-Type Pencils / S.M. Zagorodnyuk // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 16 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications (OPSFA14). The full collection is available at https://www.emis.de/journals/SIGMA/OPSFA2017.html.
The author is grateful to referees for their valuable comments and suggestions which led to an
essential improvement of the paper.
Дата:
2017
Переглядів:
472
Завантажень:
250
Анотація:
In this paper we study the inverse spectral problem for Jacobi-type pencils. By a Jacobi-type pencil we mean the following pencil J₅−λJ₃, where J₃ is a Jacobi matrix and J₅ 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.
