Ufa Mathematical Journal
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Ufimsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






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


Ufa Mathematical Journal, 2014, Volume 6, Issue 1, Pages 29–55
DOI: https://doi.org/10.13108/2014-6-1-29
(Mi ufa231)
 

This article is cited in 5 scientific papers (total in 5 papers)

Discrete spectrum of thin PTPT-symmetric waveguide

D.I. Borisovab

a Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa, Russia
b Bashkir State Pedagogical University, Ufa, Russia
References:
Abstract: In a thin multidimensional layer we consider a differential second order PTPT-symmetric operator. The operator is of rather general form and its coefficients are arbitrary functions depending both on slow and fast variables. The PTPT-symmetry of the operator is ensured by the boundary conditions of Robin type with pure imaginary coefficient. In the work we determine the limiting operator, prove the uniform resolvent convergence of the perturbed operator to the limiting one, and derive the estimates for the rates of convergence. We establish the convergence of the spectrum of perturbed operator to that of the limiting one. For the perturbed eigenvalues converging to the limiting discrete ones we prove that they are real and construct their complete asymptotic expansions. We also obtain the complete asymptotic expansions for the associated eigenfunctions.
Keywords: PTPT-symmetric operator, thin domain, uniform resolvent convergence, estimates for the rate of convergence, spectrum, asymptotic expansions.
Received: 14.08.2013
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 35P05, 35B25, 35C20
Language: English
Original paper language: Russian
Citation: D.I. Borisov, “Discrete spectrum of thin PTPT-symmetric waveguide”, Ufa Math. J., 6:1 (2014), 29–55
Citation in format AMSBIB
\Bibitem{Bor14}
\by D.I.~Borisov
\paper Discrete spectrum of thin $\mathcal{PT}$-symmetric waveguide
\jour Ufa Math. J.
\yr 2014
\vol 6
\issue 1
\pages 29--55
\mathnet{http://mi.mathnet.ru/eng/ufa231}
\crossref{https://doi.org/10.13108/2014-6-1-29}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000371149500003}
\elib{https://elibrary.ru/item.asp?id=21290425}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84899697311}
Linking options:
  • https://www.mathnet.ru/eng/ufa231
  • https://doi.org/10.13108/2014-6-1-29
  • https://www.mathnet.ru/eng/ufa/v6/i1/p30
  • This publication is cited in the following 5 articles:
    1. Borisov I D., Zezyulin D.A., “Bifurcations of Essential Spectra Generated By a Small Non-Hermitian Hole. i. Meromorphic Continuations”, Russ. J. Math. Phys., 28:4 (2021), 416–433  crossref  mathscinet  zmath  isi  scopus
    2. de Oliveira C., Verri A.A., “on the Neumann Laplacian in Nonuniformly Collapsing Strips”, Commun. Contemp. Math., 22:4 (2020), 1950021  crossref  mathscinet  zmath  isi  scopus
    3. D. I. Borisov, M. Znojil, “On eigenvalues of a PT-symmetric operator in a thin layer”, Sb. Math., 208:2 (2017), 173–199  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. R. Novak, “Bound States in Waveguides With Complex Robin Boundary Conditions”, Asymptotic Anal., 96:3-4 (2016), 251–281  crossref  zmath  isi  elib  scopus
    5. D.I. Borisov, “The Emergence of Eigenvalues of a PT-Symmetric Operator in a Thin Strip”, Math. Notes, 98:6 (2015), 872–883  mathnet  crossref  crossref  mathscinet  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Уфимский математический журнал
    Statistics & downloads:
    Abstract page:494
    Russian version PDF:237
    English version PDF:24
    References:105
     
      Contact us:
    math-net2025_02@mi-ras.ru
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025