Abstract:
The problems of completeness and basic property of systems of eigenfunctions and root functions are important questions of the spectral theory of non-self-adjoint differential operators with discrete spectra. In this paper, we give a brief survey of results on this topic for the Sturm–Liouville and Dirac operators with arbitrary two-point boundary conditions and arbitrary complex-valued summable potentials.
Citation:
A. S. Makin, “On two-point boundary-value problems for the Sturm–Liouville and Dirac operators”, Proceedings of the Voronezh spring mathematical school
“Modern methods of the theory of boundary-value problems. Pontryagin
readings – XXX”.
Voronezh, May 3-9, 2019. Part 5, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 194, VINITI, Moscow, 2021, 144–154
\Bibitem{Mak21}
\by A.~S.~Makin
\paper On two-point boundary-value problems for the Sturm--Liouville and Dirac operators
\inbook Proceedings of the Voronezh spring mathematical school
“Modern methods of the theory of boundary-value problems. Pontryagin
readings – XXX”.
Voronezh, May 3-9, 2019. Part 5
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2021
\vol 194
\pages 144--154
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into823}
\crossref{https://doi.org/10.36535/0233-6723-2021-194-144-154}
Linking options:
https://www.mathnet.ru/eng/into823
https://www.mathnet.ru/eng/into/v194/p144
This publication is cited in the following 2 articles:
E. J. Ibadov, “On the Ries inequality and the basicity of systems of root vector functions of $2m$th order Dirac-type operator with summable coefficient”, Izv. Vyssh. Uchebn. Zaved. Mat., 2024, no. 11, 23–34
E. J. Ibadov, “On the Riesz Inequality and the Basicity of Systems of Root Vector Functions of 2mth-Order Dirac-Type Operator with Summable Coefficient”, Russ Math., 68:11 (2024), 18
Citation in format AMSBIB
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