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On the Basic Property in \(L_p \) of a System of Eigenfunctions of a Problem with the Square of the Spectral Parameter in the Boundary Condition

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Abstract

We study the Sturm–Liouville problem with the square of the spectral parameter in one boundary condition, the other boundary condition being homogeneous. In the presence of a multiple eigenvalue, we establish the basis property of the system of eigenfunctions without one arbitrary function with a simple eigenvalue.

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REFERENCES

  1. Kapustin, N.Yu., On the uniform convergence of the Fourier series for a spectral problem with squared spectral parameter in a boundary condition, Differ. Equations, 2010, vol. 46, no. 10, pp. 1507–1510.

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ACKNOWLEDGMENTS

The author is grateful to Academician E.I. Moiseev for his interest in this work.

Funding

This work was financially supported by the RF Ministry of Education and Science in the framework of implementing the program of the Moscow Center for Fundamental and Applied Mathematics by Agreement no. 075-15-2019-1621 and partly supported by the Russian Foundation for Basic Research, project no. 20-51-18006 Bolg-a.

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  1. Lomonosov Moscow State University, Moscow, 119991, Russia

    N. Yu. Kapustin

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  1. N. Yu. Kapustin
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Correspondence to N. Yu. Kapustin.

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Translated by V. Potapchouck

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Kapustin, N.Y. On the Basic Property in \(L_p \) of a System of Eigenfunctions of a Problem with the Square of the Spectral Parameter in the Boundary Condition. Diff Equat 57, 1115–1118 (2021). https://doi.org/10.1134/S0012266121080140

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  • DOI: https://doi.org/10.1134/S0012266121080140

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