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Izv. Akad. Nauk SSSR Ser. Mat., 1986, Volume 50, Issue 3, Pages 435–457 (Mi izv1496)  

This article is cited in 25 scientific papers (total in 25 papers)

A theorem on splitting an operator, and some related questions in the analytic theory of perturbations

A. G. Baskakov

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.

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English version:
Mathematics of the USSR-Izvestiya, 1987, 28:3, 421–444

Bibliographic databases:

UDC: 517.983.28+519.614
MSC: Primary 47A10, 47A55; Secondary 47B40
Received: 02.04.1981
Revised: 23.02.1983

Citation: A. G. Baskakov, “A theorem on splitting an operator, and some related questions in the analytic theory of perturbations”, Izv. Akad. Nauk SSSR Ser. Mat., 50:3 (1986), 435–457; Math. USSR-Izv., 28:3 (1987), 421–444

Citation in format AMSBIB
\by A.~G.~Baskakov
\paper A~theorem on splitting an operator, and some related questions in the analytic theory of perturbations
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1986
\vol 50
\issue 3
\pages 435--457
\jour Math. USSR-Izv.
\yr 1987
\vol 28
\issue 3
\pages 421--444

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    This publication is cited in the following articles:
    1. A. G. Baskakov, “Rasscheplenie vozmuschennogo differentsialnogo operatora s neogranichennymi operatornymi koeffitsientami”, Fundament. i prikl. matem., 8:1 (2002), 1–16  mathnet  mathscinet  zmath
    2. A. G. Baskakov, “Representation theory for Banach algebras, Abelian groups, and semigroups in the spectral analysis of linear operators”, Journal of Mathematical Sciences, 137:4 (2006), 4885–5036  mathnet  crossref  mathscinet  zmath  elib
    3. A. G. Baskakov, A. V. Derbushev, A. O. Shcherbakov, “The method of similar operators in the spectral analysis of non-self-adjoint Dirac operators with non-smooth potentials”, Izv. Math., 75:3 (2011), 445–469  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. A. G. Baskakov, “Analysis of linear differential equations by methods of the spectral theory of difference operators and linear relations”, Russian Math. Surveys, 68:1 (2013), 69–116  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. A. V. Karpikova, “Asymptotics for eigenvalues of Sturm–Liouville operator with periodic boundary conditions”, Ufa Math. J., 6:3 (2014), 28–34  mathnet  crossref  mathscinet  elib
    6. E. Yu. Romanova, “Spectral Analysis of Differential Operator with Involution”, J. Math. Sci., 213:6 (2016), 897–909  mathnet  crossref
    7. D. M. Polyakov, “Spectral analysis of a fourth-order nonselfadjoint operator with nonsmooth coefficients”, Siberian Math. J., 56:1 (2015), 138–154  mathnet  crossref  mathscinet  isi  elib  elib
    8. D. M. Polyakov, “Method of similar operators in spectral analysis of a fourth-order nonself-adjoint operator”, Diff Equat, 51:3 (2015), 421  crossref
    9. A. G. Baskakov, “Estimates for the Green's function and parameters of exponential dichotomy of a hyperbolic operator semigroup and linear relations”, Sb. Math., 206:8 (2015), 1049–1086  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    10. D. M. Polyakov, “Spectral analysis of a fourth order differential operator with periodic and antiperiodic boundary conditions”, St. Petersburg Math. J., 27:5 (2016), 789–811  mathnet  crossref  mathscinet  isi  elib
    11. N. B. Uskova, “On spectral properties of Sturm–Liouville operator with matrix potential”, Ufa Math. J., 7:3 (2015), 84–94  mathnet  crossref  isi  elib
    12. A. G. Baskakov, D. M. Polyakov, “Spectral Properties of the Hill Operator”, Math. Notes, 99:4 (2016), 598–602  mathnet  crossref  crossref  mathscinet  isi  elib
    13. 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  mathnet  crossref  mathscinet  elib
    14. Polyakov D.M., “Spectral properties of an even-order differential operator”, Differ. Equ., 52:8 (2016), 1098–1103  crossref  mathscinet  zmath  isi  elib  scopus
    15. 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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    16. 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  mathnet  crossref  isi
    17. 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  crossref  isi
    18. 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  mathnet  crossref  isi
    19. 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  mathnet  crossref
    20. D. M. Polyakov, “A one-dimensional Schrödinger operator with square-integrable potential”, Siberian Math. J., 59:3 (2018), 470–485  mathnet  crossref  crossref  isi  elib
    21. N. B. Uskova, G. V. Garkavenko, “Teorema o rasscheplenii lineinykh operatorov i asimptotika sobstvennykh znachenii raznostnykh operatorov s rastuschim potentsialom”, Sib. zhurn. chist. i prikl. matem., 18:1 (2018), 91–106  mathnet  crossref
    22. 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  mathnet  crossref  isi
    23. 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  crossref  mathscinet  zmath  isi
    24. N. B. Uskova, “Matrichnyi analiz spektralnykh proektorov vozmuschennykh samosopryazhennykh operatorov”, Sib. elektron. matem. izv., 16 (2019), 369–405  mathnet  crossref
    25. 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  crossref  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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