Direct and inverse spectral problems for a class of non-self-adjoint periodic tridiagonal matrices

被引：2
作者：
Bebiano, Natalia [1 ]
Tyaglov, Mikhail [2 ]
机构：
[1] Univ Coimbra, Dept Matemat, P-3001454 Coimbra, Portugal
[2] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2013年 / 439卷 / 11期
关键词：
Inverse eigenvalue problem; Stable polynomials; Hermite-Biehler theorem; Jacobi matrix; Periodic Jacobi matrix; CONTINUED FRACTIONS; JACOBI MATRICES;
D O I：
10.1016/j.laa.2013.09.026
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The spectral properties of a class of tridiagonal matrices are investigated. The reconstruction of matrices of this special class from given spectral data is also studied. Necessary and sufficient conditions for that reconstruction are found. The obtained results extend some results on the direct and inverse spectral problems for periodic Jacobi matrices and for some non-self-adjoint tridiagonal matrices. (C) 2013 Elsevier Inc. All rights reserved.
引用
收藏
页码：3490 / 3504
页数：15
相关论文
共 21 条
[1]  
Akhiezer N. L., 1965, The Classical Momentum Problem
[2]   CONTINUED FRACTIONS AND PERIODIC JACOBI MATRICES [J].
ANDREA, SA ;
BERRY, TG .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1992, 161 :117-134
[3]  
Arlinskii Y, 2011, OPER THEORY ADV APPL, V217, P1, DOI 10.1007/978-3-7643-9996-2
[4]   Non-self-adjoint Jacobi matrices with a rank-one imaginary part [J].
Arlinskii, Yury ;
Tsekanovskii, Eduard .
JOURNAL OF FUNCTIONAL ANALYSIS, 2006, 241 (02) :383-438
[5]   Complex Jacobi matrices [J].
Beckermann, B .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2001, 127 (1-2) :17-65
[6]  
BOLEY D, 1984, MATH COMPUT, V42, P143, DOI 10.1090/S0025-5718-1984-0725989-1
[7]  
FERGUSON WE, 1980, MATH COMPUT, V35, P1203, DOI 10.1090/S0025-5718-1980-0583498-3
[8]   m-functions and inverse spectral analysis for finite and semi-infinite Jacobi matrices [J].
Gesztesy, F ;
Simon, B .
JOURNAL D ANALYSE MATHEMATIQUE, 1997, 73 :267-297
[9]  
Gladwell G.M.L., 1986, DYNAMICAL SYSTEMS, V9
[10]   INVERSE EIGENVALUE PROBLEMS FOR JACOBI MATRICES [J].
HALD, OH .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1976, 14 (01) :63-85
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