Persymmetric Jacobi matrices, isospectral deformations and orthogonal polynomials

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:450

Article

Genest, Vincent X.¹  Tsujimoto, Satoshi²  Vinet, Luc³  Zhedanov, Alexei⁴ 

[1] MIT, Dept Math, 77 Massachusetts Ave, Cambridge, MA 02139 USA

[2] Kyoto Univ, Grad Sch Informat, Dept Appl Math & Phys, Sakyo Ku, Yoshida Honmachi, Kyoto 6068501, Japan

[3] Univ Montreal, Ctr Rech Math, Ctr Ville Stn, POB 6128, Montreal, PQ H3C 3J7, Canada

[4] Renmin Univ China, Sch Informat, Dept Math, Beijing 100872, Peoples R China

关键词: Persymmetric matrices;    Inverse spectral problems;    Orthogonal polynomials;    Isospectral deformations;   

DOI  :  10.1016/j.jmaa.2017.01.056

来源: Elsevier

【 摘 要 】

Persymmetric Jacobi matrices are invariant under reflection with respect to the anti diagonal. The associated orthogonal polynomials have distinctive properties that are discussed. They are found in particular to be also orthogonal on the restrictions either to the odd or to the even points of the complete orthogonality lattice. This is exploited to design very efficient inverse problem algorithms for the reconstruction of persymmetric Jacobi matrices from spectral points. Isospectral deformations of such matrices are also considered. Expressions for the associated polynomials and their weights are obtained in terms of the undeformed entities. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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