Inverse spectral analysis for a class of infinite band symmetric matrices

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:445

Article

Kudryavtsev, Mikhail¹  Palafox, Sergio²  Silva, Luis O.² 

[1] Inst Low Temp Phys & Engn, Dept Math, Lenin Av 47, UA-61108 Kharkov, Ukraine

[2] Univ Nacl Autonoma Mexico, Inst Invest Matemat Aplicadas & Sistemas, Dept Fis Matemat, Mexico City 04510, DF, Mexico

关键词: Inverse spectral problem;    Band symmetric matrices;    Spectral measure;   

DOI  :  10.1016/j.jmaa.2016.07.057

来源: Elsevier

【 摘 要 】

This work deals with the direct and inverse spectral analysis for a class of infinite band symmetric matrices. This class corresponds to operators arising from difference equations with usual and inner boundary conditions. We give a characterization of the spectral functions for the operators and provide necessary and sufficient conditions for a matrix-valued function to be a spectral function of the operators. Additionally, we give an algorithm for recovering the matrix from the spectral function. The approach to the inverse problem is based on the rational interpolation theory. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free