Abstract:
In the work we obtain asymptotic estimates for the eigenvalues, eigenvectors and spectral projectors of a Sturm–Liouville operator with a matrix potential subject to quasi-periodic boundary conditions. The matrix potential is formed by functions square summable on the segment [0,1] and the matrix of the means of the functions have simple eigenvalues. We consider also the case when the matrix of the means has a simple structure.
Keywords:
similar operator method, spectrum, linear operators, spectral projectors.
\Bibitem{Usk15}
\by N.~B.~Uskova
\paper On spectral properties of Sturm--Liouville operator with matrix potential
\jour Ufa Math. J.
\yr 2015
\vol 7
\issue 3
\pages 84--94
\mathnet{http://mi.mathnet.ru/eng/ufa294}
\crossref{https://doi.org/10.13108/2015-7-3-84}
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Linking options:
https://www.mathnet.ru/eng/ufa294
https://doi.org/10.13108/2015-7-3-84
https://www.mathnet.ru/eng/ufa/v7/i3/p88
This publication is cited in the following 13 articles:
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
D. M. Polyakov, “Spectral estimates for the fourth-order operator with matrix coefficients”, Comput. Math. Math. Phys., 60:7 (2020), 1163–1184
D. M. Polyakov, “On the Spectral Characteristics of Non-Self-Adjoint Fourth-Order Operators with Matrix Coefficients”, Math. Notes, 105:4 (2019), 630–635
N. B. Uskova, “Matrichnyi analiz spektralnykh proektorov vozmuschennykh samosopryazhennykh operatorov”, Sib. elektron. matem. izv., 16 (2019), 369–405
I. N. Braeutigam, D. M. Polyakov, “Asymptotics of eigenvalues of infinite block matrices”, Ufa Math. J., 11:3 (2019), 11–28
A. G. Baskakov, N. B. Uskova, “Fourier method for first order differential equations with involution and groups of operators”, Ufa Math. J., 10:3 (2018), 11–34
A. G. Baskakov, I. A. Krishtal, N. B. Uskova, “Linear differential operator with an involution as a generator of an operator group”, Oper. Matrices, 12:3 (2018), 723–756
I. N. Braeutigam, D. M. Polyakov, “On the asymptotics of eigenvalues of a fourth-order differential operator with matrix coefficients”, Differ. Equ., 54:4 (2018), 450–467
N. B. Uskova, G. V. Garkavenko, “The theorem on the decomposition of linear operators and the asymptotic behavior of the eigenvalues of difference operators with a growing potential”, J. Math. Sci., 246:6 (2020), 812–827
G. V. Garkavenko, N. B. Uskova, “Metod podobnykh operatorov v issledovanii spektralnykh svoistv raznostnykh operatorov s rastuschim potentsialom”, Sib. elektron. matem. izv., 14 (2017), 673–689
G. V. Garkavenko, N. B. Uskova, “Asimptotika sobstvennykh znachenii raznostnogo operatora s rastuschim potentsialom i polugruppy operatorov”, Matematicheskaya fizika i kompyuternoe modelirovanie, 20:4 (2017), 6–17
G. V. Garkavenko, N. B. Uskova, “Spektralnyi analiz odnogo klassa raznostnykh operatorov s rastuschim potentsialom”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 16:4 (2016), 395–402
N. B. Uskova, “On the Spectral Properties of a Second-Order Differential Operator With a Matrix Potential”, Differ. Equ., 52:5 (2016), 557–567
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