Abstract:
The basis for most of the results in this paper is a theorem that a perturbed operator with disjoint parts of the spectrum is similar to an operator for which the subspaces constructed from the isolated parts of the unperturbed operator are invariant. In particular, estimates are obtained for the eigenvalues and projections of the perturbed operators, results about equiconvergence of spectral decompositions are obtained, and convergence questions for the eigenvalues are investigated with the use of projection methods.
Bibliography: 15 titles.
Citation:
A. G. Baskakov, “A theorem on splitting an operator, and some related questions in the analytic theory of perturbations”, Math. USSR-Izv., 28:3 (1987), 421–444
\Bibitem{Bas86}
\by A.~G.~Baskakov
\paper A~theorem on splitting an operator, and some related questions in the analytic theory of perturbations
\jour Math. USSR-Izv.
\yr 1987
\vol 28
\issue 3
\pages 421--444
\mathnet{http://mi.mathnet.ru/eng/im1496}
\crossref{https://doi.org/10.1070/IM1987v028n03ABEH000891}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=854591}
\zmath{https://zbmath.org/?q=an:0636.47019}
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https://www.mathnet.ru/eng/im1496
https://doi.org/10.1070/IM1987v028n03ABEH000891
https://www.mathnet.ru/eng/im/v50/i3/p435
This publication is cited in the following 33 articles:
Dmitry M. Polyakov, “Spectral analysis of an even order differential operator with square integrable potential”, Math Methods in App Sciences, 46:5 (2023), 5483
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
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
N. B. Uskova, “Matrichnyi analiz spektralnykh proektorov vozmuschennykh samosopryazhennykh operatorov”, Sib. elektron. matem. izv., 16 (2019), 369–405
Baskakov A.G. Krishtal I.A. Uskova N.B., “Similarity Techniques in the Spectral Analysis of Perturbed Operator Matrices”, J. Math. Anal. Appl., 477:2 (2019), 930–960
I. A. Krishtal, N. B. Uskova, “Spektralnye svoistva differentsialnykh operatorov pervogo poryadka s involyutsiei i gruppy operatorov”, Sib. elektron. matem. izv., 16 (2019), 1091–1132
A. G. Baskakov, I. A. Krishtal, N. B. Uskova, “Metod podobnykh operatorov v issledovanii spektralnykh svoistv vozmuschennykh differentsialnykh operatorov pervogo poryadka”, Materialy Voronezhskoi zimnei matematicheskoi shkoly «Sovremennye metody teorii funktsii i smezhnye problemy». 28 yanvarya–2 fevralya 2019 g. Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 171, VINITI RAN, M., 2019, 3–18
D. M. Polyakov, “A one-dimensional Schrödinger operator with square-integrable potential”, Siberian Math. J., 59:3 (2018), 470–485
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
Baskakov A.G. Krishtal I.A. Uskova N.B., “Linear Differential Operator With An Involution as a Generator of An Operator Group”, Oper. Matrices, 12:3 (2018), 723–756
A. N. Shelkovoi, “Spektralnye svoistva differentsialnogo operatora vtorogo poryadka, opredelyaemogo nelokalnymi kraevymi usloviyami”, Matematicheskaya fizika i kompyuternoe modelirovanie, 21:4 (2018), 18–33
Serge Kozlukov, “The method of similar operators in the study of the spectra of the adjacency matrices of graphs”, J. Phys.: Conf. Ser., 973 (2018), 012036
I. N. Braeutigam, D. M. Polyakov, “On the Asymptotics of Eigenvalues of a Fourth-Order Differential Operator with Matrix Coefficients”, Diff Equat, 54:4 (2018), 450
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
A. G. Baskakov, D. M. Polyakov, “The method of similar operators in the spectral analysis of the Hill operator with nonsmooth potential”, Sb. Math., 208:1 (2017), 1–43
A. G. Baskakov, T. K. Katsaran, T. I. Smagina, “Linear differential second-order equations in Banach space and splitting of operators”, Russian Math. (Iz. VUZ), 61:10 (2017), 32–43
Baskakov A.G. Krishtal I.A. Romanova E.Yu., “Spectral Analysis of a Differential Operator With An Involution”, J. Evol. Equ., 17:2 (2017), 669–684
Garkavenko G.V., Uskova N.B., “Method of Similar Operators in Research of Spectral Properties of Difference Operators With Growthing Potential”, Sib. Electron. Math. Rep., 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
A. G. Baskakov, D. M. Polyakov, “Spectral Properties of the Hill Operator”, Math. Notes, 99:4 (2016), 598–602
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