New York Journal of Mathematics
Volume 23 (2017) 1141-1171


Mikhail Kudryavtsev, Sergio Palafox, and Luis O. Silva

Inverse spectral analysis for a class of finite band symmetric matrices

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Published: September 5, 2017
Keywords: Inverse spectral problem, band symmetric matrices, spectral measure
Subject: 34K29, 47B36

In this note, we solve an inverse spectral problem for a class of finite band symmetric matrices. We provide necessary and sufficient conditions for a matrix valued function to be a spectral function of the operator corresponding to a matrix in our class and give an algorithm for recovering this matrix from the spectral function. The reconstructive algorithm is applicable to matrices which cannot be treated by known inverse block matrix methods. Our approach to the inverse problem is based on the rational interpolation theory developed in a previous paper.


Research partially supported by UNAM-DGAPA-PAPIIT IN105414

Author information

Mikhail Kudryavtsev:
Department of Mathematics, Institute for Low Temperature Physics and Engineering, Lenin Av. 47, 61103, Kharkov, Ukraine

Sergio Palafox:
Instituto de Física y Matemáticas, Universidad Tecnológica de la Mixteca, Km. 2.5 Carr. a Acatlima, C.P. 69000, Oaxaca, México

Luis O. Silva:
Departamento de Física Matemática, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, C.P. 04510, México D.F.