È. F. Akhmerova, “Asymptotics of the Spectrum of Nonsmooth Perturbations of Differential Operators of Order $2m$”, Mat. Zametki, 90:6 (2011), 833–844; Math. Notes, 90:6 (2011), 813

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Matematicheskie Zametki, 2011, Volume 90, Issue 6, Pages 833–844
DOI: https://doi.org/10.4213/mzm8407 (Mi mzm8407)

This article is cited in 12 scientific papers (total in 12 papers)

Asymptotics of the Spectrum of Nonsmooth Perturbations of Differential Operators of Order

2 m

$2m$

È. F. Akhmerova

Bashkir State University

Full-text PDF (448 kB) Citations (12)

References:

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DOI: https://doi.org/10.4213/mzm8407

Abstract: On a finite closed interval, we obtain the asymptotics of the eigenvalues of a differential operator of order

2 m

$2m$ perturbed by a differential operator of order

2 m - 2

$2m-2$ given by a quasidifferential expression. We also consider the case of multiple eigenvalues.

Keywords: perturbation of a differential operator, spectrum of perturbations, quasidifferential expression, Hilbert space, Dirichlet boundary conditions, resolvent of an operator.

Received: 27.04.2009
Revised: 25.02.2010

English version:
Mathematical Notes, 2011, Volume 90, Issue 6, Pages 813–823
DOI: https://doi.org/10.1134/S0001434611110216

Bibliographic databases:

Document Type: Article

UDC: 517.984

Language: Russian

Citation: È. F. Akhmerova, “Asymptotics of the Spectrum of Nonsmooth Perturbations of Differential Operators of Order

2 m

$2m$ ”, Mat. Zametki, 90:6 (2011), 833–844; Math. Notes, 90:6 (2011), 813–823

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm8407

https://doi.org/10.4213/mzm8407

https://www.mathnet.ru/eng/mzm/v90/i6/p833

This publication is cited in the following 12 articles:

E. F. Akhmerova, M. A. Rakhmatzoda, T. G. Amangildin, “Formula regulyarizovannogo sleda differentsialnogo operatora $2m$ -go poryadka s periodicheskimi granichnymi usloviyami”, Izv. vuzov. Matem., 2024, no. 5, 85–90
E. F. Akhmerova, M. A. Rahmatzoda, T. G. Amangildin, “Formula for Regularized Trace of 2m-Order Differential Operator with Periodic Boundary Conditions”, Russ Math., 68:5 (2024), 72
Dmitry M. Polyakov, “Spectral asymptotics and a trace formula for a fourth-order differential operator corresponding to thin film equation”, Monatsh Math, 202:1 (2023), 171
Dmitry M. Polyakov, “Spectral analysis of an even order differential operator with square integrable potential”, Math Methods in App Sciences, 46:5 (2023), 5483
Lu Chen, Guoliang Shi, Jun Yan, “On the Hochstadt–Lieberman theorem for the fourth-order binomial operator”, Journal of Mathematical Physics, 64:4 (2023)
Natalia P. Bondarenko, “SPECTRAL DATA ASYMPTOTICS FOR THE HIGHER-ORDER DIFFERENTIAL OPERATORS WITH DISTRIBUTION COEFFICIENTS”, J Math Sci, 266:5 (2022), 794
Dmitry M. Polyakov, “Sharp eigenvalue asymptotics of fourth-order differential operators”, ASY, 130:3-4 (2022), 477
N. B. Uskova, “Matrichnyi analiz spektralnykh proektorov vozmuschennykh samosopryazhennykh operatorov”, Sib. elektron. matem. izv., 16 (2019), 369–405
D. M. Polyakov, “A one-dimensional Schrödinger operator with square-integrable potential”, Siberian Math. J., 59:3 (2018), 470–485
Polyakov D.M., “Spectral properties of an even-order differential operator”, Differ. Equ., 52:8 (2016), 1098–1103
Badanin A. Korotyaev E., “Trace Formulas For Fourth Order Operators on Unit Interval, II”, Dyn. Partial Differ. Equ., 12:3 (2015), 217–239
Badanin A. Korotyaev E., “Inverse Problems and Sharp Eigenvalue Asymptotics For Euler-Bernoulli Operators”, Inverse Probl., 31:5 (2015), 055004

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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