On two-point boundary-value problems for the Sturm--Liouville and Dirac operators
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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, Tome 194 (2021), pp. 144-154
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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.
Keywords:
Sturm–Liouville operator, Dirac operator, boundary-value problem, completeness, basis property.
@article{INTO_2021_194_a12,
author = {A. S. Makin},
title = {On two-point boundary-value problems for the {Sturm--Liouville} and {Dirac} operators},
journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
pages = {144--154},
publisher = {mathdoc},
volume = {194},
year = {2021},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/INTO_2021_194_a12/}
}
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A. S. Makin. On two-point boundary-value problems for the Sturm--Liouville and Dirac operators. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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, Tome 194 (2021), pp. 144-154. http://geodesic.mathdoc.fr/item/INTO_2021_194_a12/