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Direct and Inverse Problems for the Matrix Sturm–Liouville Operator with General Self-Adjoint Boundary Conditions

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Abstract

The matrix Sturm–Liouville operator on a finite interval with boundary conditions in general self-adjoint form and with singular potential of class \(W_2^{-1}\) is studied. This operator generalizes Sturm–Liouville operators on geometrical graphs. We investigate structural and asymptotical properties of the spectral data (eigenvalues and weight matrices) of this operator. Furthermore, we prove the uniqueness of recovering the operator from its spectral data, by using the method of spectral mappings.

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Funding

This work was supported by the Russian Science Foundation under grant 19-71-00009.

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Authors and Affiliations

  1. Samara National Research University, Samara, 443086, Russia

    N. P. Bondarenko

  2. Saratov State University, Saratov, 410012, Russia

    N. P. Bondarenko

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  1. N. P. Bondarenko
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Bondarenko, N.P. Direct and Inverse Problems for the Matrix Sturm–Liouville Operator with General Self-Adjoint Boundary Conditions. Math Notes 109, 358–378 (2021). https://doi.org/10.1134/S0001434621030044

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