Abstract
We study the first boundary value problem for a second-order differential operator with a singular coefficient on an interval with transmission conditions at an interior point. Asymptotic formulas are obtained for the eigenfunctions and eigenvalues of both the original and the adjoint operator. The completeness and unconditional basis property of the eigenfunction systems of these operators in the space of square integrable functions on the interval are established. Il’in’s method and Il’in’s conditions are applied to establish the Bessel inequality.
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Funding
This work was supported by the Ministry of Science and Higher Education of the Russian Federation within the framework of the program of the Moscow Center for Fundamental and Applied Mathematics under agreement no. 075-15-2022-284.
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Translated by V. Potapchouck
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Lomov, I.S. Spectral Properties of a Singular Differential Operator on an Interval with Transmission Conditions. Diff Equat 59, 591–596 (2023). https://doi.org/10.1134/S0012266123050026
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DOI: https://doi.org/10.1134/S0012266123050026