Sbornik: Mathematics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Sbornik: Mathematics, 2017, Volume 208, Issue 1, Pages 1–43
DOI: https://doi.org/10.1070/SM8637 (Mi sm8637) 		 
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
English version PDF (698 kB) Citations (45)
References:
PDF
HTML
DOI: https://doi.org/10.1070/SM8637
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.
Funding agency Grant number
Russian Science Foundation 14-21-00066
This work was supported by the Russian Science Foundation (grant no. 14-21-00066).
Received: 21.11.2015
Russian version:
Matematicheskii Sbornik, 2017, Volume 208, Number 1, Pages 3–47
DOI: https://doi.org/10.4213/sm8637
Bibliographic databases:
Document Type: Article
UDC: 517.927
MSC: 47A55, 47B40, 34L10, 34L20, 34L40
Language: English
Original paper language: Russian
Citation: A. G. Baskakov, D. M. Polyakov, “The method of similar operators in the spectral analysis of the Hill operator with nonsmooth potential”, Mat. Sb., 208:1 (2017), 3–47; Sb. Math., 208:1 (2017), 1–43
Citation in format AMSBIB
\Bibitem{BasPol17}
\by A.~G.~Baskakov, D.~M.~Polyakov
\paper The method of similar operators in the spectral analysis of the Hill operator with nonsmooth potential
\jour Mat. Sb.
\yr 2017
\vol 208
\issue 1
\pages 3--47
\mathnet{http://mi.mathnet.ru/sm8637}
\crossref{https://doi.org/10.4213/sm8637}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3598763}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2017SbMat.208....1B}
\elib{https://elibrary.ru/item.asp?id=28172152}
\transl
\jour Sb. Math.
\yr 2017
\vol 208
\issue 1
\pages 1--43
\crossref{https://doi.org/10.1070/SM8637}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000397338200001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85016588047}
Linking options:
  • https://www.mathnet.ru/eng/sm8637
  • https://doi.org/10.1070/SM8637
  • https://www.mathnet.ru/eng/sm/v208/i1/p3
    • This publication is cited in the following 45 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:1410
    Russian version PDF:149
    English version PDF:21
    References:143
    First page:197
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024