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JOURNALS // Algebra i Analiz // Archive

Algebra i Analiz, 2019 Volume 31, Issue 4, Pages 16–47 (Mi aa1661)

This article is cited in 8 papers

Research Papers

On the asymptotics of eigenvalues of a third-order differential operator

I. N. Braeutigama, D. M. Polyakovbc

a Northern (Arctic) Federal University named after M. V. Lomonosov, Arkhangelsk
b Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa
c Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz

Abstract: We consider a third-order nonselfadjoint differential operator with square summable coefficients whose domain is defined by quasiperiodic boundary conditions. For this operator, using the method of similar operators, we obtain an asymptotic behavior of eigenvalues, estimates of the deviations of spectral projections, and the equiconvergence of spectral decompositions.

Keywords: third-order differential operator, spectrum, asymptotic behavior of eigenvalues, equiconvergence of spectral decompositions.

MSC: Primary 47A75; Secondary 47A10, 65L10

Received: 17.05.2018


 English version:
St. Petersburg Mathematical Journal, 2020, 31:4, 585–606

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© Steklov Math. Inst. of RAS, 2024