Spectral analysis of infinite Marchenko-Slavin matrices

• Autorzy: Palafox Sergio , Silva Luis O.

Identyfikatory

DOI

10.7494/OpMath.2025.45.2.227

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

inverse spectral problem; band symmetric matrices; spectral measure

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2025
• Tom: Vol. 45, no. 2
• Strony: 227--249
• Opis fizyczny: Bibliogr. 12 poz., rys.

Twórcy

autor

Palafox Sergio

• Universidad Tecnológica de la Mixteca, Centro de Modelación Matemática, Vinculación y Consultoría, Huajuapan de León, Oaxaca, México, C.P. 69004

• https://orcid.org/0000-0002-4961-4834

autor

Silva Luis O.

• Universidad Nacional Autónoma de México, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Departamento de Física Matemática, Ciudad de México, C.P. 04510

• https://orcid.org/0000-0002-9028-606X

Bibliografia

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• [3] M.Sh. Birman, M.Z. Solomjak, Spectral Theory of Selfadjoint Operators in Hilbert Space, Mathematics and its Applications (Soviet Series), D. Reidel Publishing Co., Dordrecht, 1987.
• [4] M.S. Brodski˘ı, Triangular and Jordan Representations of Linear Operators, American Mathematical Society, Providence, R.I., 1971.
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• [7] M. Kudryavtsev, S. Palafox, L.O. Silva, On a linear interpolation problem for n-dimensional vector polynomials, J. Approx. Theory 199 (2015), 45–62.
• [8] M. Kudryavtsev, S. Palafox, L.O. Silva, Inverse spectral analysis for a class of finite band symmetric matrices, New York J. Math. 23 (2017), 1141–1171.
• [9] M. Kudryavtsev, S. Palafox, L.O. Silva, Inverse spectral analysis for a class of infinite band symmetric matrices, J. Math. Anal. Appl. 445 (2017), no. 1, 762–783.
• [10] V. Marchenko, V. Slavin, Inverse Problems in the Theory of Small Oscillations, Translations of Mathematical Monographs, vol. 247, American Mathematical Society, Providence, RI, 2018.
• [11] R. del Rio, M. Kudryavtsev, Inverse problems for Jacobi operators: I. Interior mass-spring perturbations in finite systems, Inverse Problems 28 (2012), no. 5, 055007.
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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025)