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This article is cited in 45 scientific papers (total in 45 papers)
The method of similar operators in the spectral analysis of the Hill operator with nonsmooth potential
A. G. Baskakova, D. M. Polyakovb a Voronezh State University
b Research Institute for Mathematics, Voronezh State University
Abstract:
The paper is concerned with the spectral properties of second-order differential operators defined by periodic and quasi-periodic boundary conditions. We obtain asymptotic formulae for the eigenvalues, derive estimates of projections, give estimates for the equiconvergence of spectral decompositions, find sufficient conditions for operators to be spectral, and write down an asymptotic expansion for the semigroup of operators generated by the negative of the differential operator under consideration. Our estimates involve coefficients of the Fourier potential. The main results of the paper are obtained by using the method of similar operators.
Bibliography: 34 titles.
Keywords:
spectrum of an operator, method of similar operators, Hill's differential operator, asymptotic behaviour of eigenvalues, semigroup of operators.
Received: 21.11.2015
Citation:
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
Linking options:
https://www.mathnet.ru/eng/sm8637https://doi.org/10.1070/SM8637 https://www.mathnet.ru/eng/sm/v208/i1/p3
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Abstract page: | 1486 | Russian version PDF: | 170 | English version PDF: | 33 | References: | 164 | First page: | 197 |
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