Abstract:
We study first-order differential operators with an involution and non-periodic boundary conditions. We exhibit their spectral properties such as the asymptotic estimates of their eigenvalues, eigenvectors and spectral projections. We also use these properties to estimate the groups generated by the differential operators we study. The results were obtained by using the method of similar operators.
Keywords and phrases:
the method of similar operators, differential operator with an involution.
Citation:
A. G. Baskakov, I. A. Krishtal, N. B. Uskova, “On the spectral analysis of a differential operator with an involution and general boundary conditions”, Eurasian Math. J., 11:2 (2020), 30–39
\Bibitem{BasKriUsk20}
\by A.~G.~Baskakov, I.~A.~Krishtal, N.~B.~Uskova
\paper On the spectral analysis of a differential operator with an involution and general boundary conditions
\jour Eurasian Math. J.
\yr 2020
\vol 11
\issue 2
\pages 30--39
\mathnet{http://mi.mathnet.ru/emj363}
\crossref{https://doi.org/10.32523/2077-9879-2020-11-2-30-39}
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Linking options:
https://www.mathnet.ru/eng/emj363
https://www.mathnet.ru/eng/emj/v11/i2/p30
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A. G. Baskakov, G. V. Garkavenko, N. B. Uskova, “Primenenie metoda podobnykh operatorov k nekotorym klassam raznostnykh operatorov”, Differentsialnye uravneniya i matematicheskaya fizika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 225, VINITI RAN, M., 2023, 14–27
A. G. Baskakov, G. V. Garkavenko, N. B. Uskova, “Ob ogranichennykh raznostnykh operatorakh s involyutsiei”, Materialy Voronezhskoi mezhdunarodnoi zimnei matematicheskoi shkoly «Sovremennye metody teorii funktsii i smezhnye problemy», Voronezh, 27 yanvarya — 1 fevralya 2023 g. Chast 3, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 229, VINITI RAN, M., 2023, 12–21
A. G. Baskakov, I. A. Krishtal, N. B. Uskova, “O sglazhivanii operatornogo koeffitsienta differentsialnogo operatora pervogo poryadka v banakhovom prostranstve”, Materialy Voronezhskoi mezhdunarodnoi zimnei matematicheskoi shkoly «Sovremennye metody teorii funktsii i smezhnye problemy», Voronezh, 28 yanvarya – 2 fevralya 2021 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 206, VINITI RAN, M., 2022, 3–14
G. V. Garkavenko, N. B. Uskova, “O spektralnykh svoistvakh odnogo raznostnogo operatora s involyutsiei”, Materialy Voronezhskoi mezhdunarodnoi vesennei matematicheskoi shkoly «Sovremennye metody teorii kraevykh zadach. Pontryaginskie chteniya–XXXII», Voronezh, 3–9 maya 2021 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 208, VINITI RAN, M., 2022, 15–23
K. I. Usmanov, B. Kh. Turmetov, K. Zh. Nazarova, “On Solvability of a Boundary Value Problem for a Nonlocal Biharmonic Equation with a Fractional Order Boundary Operator”, Lobachevskii J Math, 43:11 (2022), 3298
Batirkhan Turmetov, Valery Karachik, “Construction of Eigenfunctions to One Nonlocal Second-Order Differential Operator with Double Involution”, Axioms, 11:10 (2022), 543
Kairat Usmanov, Batirkhan Turmetov, Kulzina Nazarova, “On the Solvability of Some Boundary Value Problems for the Nonlocal Poisson Equation with Boundary Operators of Fractional Order”, Fractal Fract, 6:6 (2022), 308
Natalia P. Bondarenko, “Inverse spectral problems for functional-differential operators with involution”, Journal of Differential Equations, 318 (2022), 169
B. Turmetov, V. Karachik, “On eigenfunctions and eigenvalues of a nonlocal Laplace operator with multiple involution”, Symmetry-Basel, 13:10 (2021), 1781
B. Turmetov, V. Karachik, M. Muratbekova, “On a boundary value problem for the biharmonic equation with multiple involutions”, Mathematics, 9:17 (2021), 2020
G Garkavenko, N Uskova, “Spectral analysis of one class perturbed first order differential operators”, J. Phys.: Conf. Ser., 1902:1 (2021), 012035
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