Opuscula Math. 45, no. 2 (2025), 227-249
https://doi.org/10.7494/OpMath.2025.45.2.227
Opuscula Mathematica
Spectral analysis of infinite Marchenko-Slavin matrices
Abstract. This work tackles the problem of spectral characterization of a class of infinite matrices arising from the modeling of small oscillations in a system of interacting particles. The class of matrices under discussion corresponds to the infinite Marchenko-Slavin class. The spectral functions of these matrices are completely characterized, and an algorithm is provided for the reconstruction of the matrix from its spectral function. The techniques used in this work are based on recent results for the spectral characterization of infinite band symmetric matrices with so-called degenerations.
Keywords: inverse spectral problem, band symmetric matrices, spectral measure.
Mathematics Subject Classification: 34K29, 47B39, 70F17.
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- Sergio Palafox
https://orcid.org/0000-0002-4961-4834- Universidad Tecnológica de la Mixteca, Centro de Modelación Matemática, Vinculación y Consultoría, Huajuapan de León, Oaxaca, México, C.P. 69004
- Luis O. Silva (corresponding author)
- https://orcid.org/0000-0002-9028-606X
- Universidad Nacional Autónoma de México, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Departamento de Física Matemática, Ciudad de México, C.P. 04510
- Communicated by P.A. Cojuhari.
- Received: 2025-01-19.
- Revised: 2025-02-06.
- Accepted: 2025-02-06.
- Published online: 2025-03-10.
