RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Funktsional. Anal. i Prilozhen.:
Year:
Volume:
Issue:
Page:
Find






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


Funktsional. Anal. i Prilozhen., 2018, Volume 52, Issue 1, Pages 80–84 (Mi faa3491)  

This article is cited in 1 scientific paper (total in 1 paper)

Brief communications

Essential Spectrum of Schrödinger Operators on Periodic Graphs

V. S. Rabinovich

Instituto Politécnico Nacional, ESIME Zacatenco, Mexico City, the United Mexican States, Mexico

Abstract: We give a description of the essential spectra of unbounded operators $\mathcal{H}_{q}$ on $L^{2}(\Gamma)$ determined by the Schrödinger operators $-d^{2}/dx^{2}+q(x)$ on the edges of $\Gamma$ and general vertex conditions. We introduce a set of limit operators of $\mathcal{H}_{q}$ such that the essential spectrum of $\mathcal{H}_{q}$ is the union of the spectra of limit operators. We apply this result to describe the essential spectra of the operators $\mathcal{H}_{q}$ with periodic potentials perturbed by terms slowly oscillating at infinity.

Keywords: periodic graph, Schrödinger operator on a graph, limit operator, essential spectrum.

DOI: https://doi.org/10.4213/faa3491

Full text: PDF file (143 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Functional Analysis and Its Applications, 2018, 52:1, 66–69

Bibliographic databases:

UDC: 517.95
Received: 13.01.2017

Citation: V. S. Rabinovich, “Essential Spectrum of Schrödinger Operators on Periodic Graphs”, Funktsional. Anal. i Prilozhen., 52:1 (2018), 80–84; Funct. Anal. Appl., 52:1 (2018), 66–69

Citation in format AMSBIB
\Bibitem{Rab18}
\by V.~S.~Rabinovich
\paper Essential Spectrum of Schr\"odinger Operators on Periodic Graphs
\jour Funktsional. Anal. i Prilozhen.
\yr 2018
\vol 52
\issue 1
\pages 80--84
\mathnet{http://mi.mathnet.ru/faa3491}
\crossref{https://doi.org/10.4213/faa3491}
\elib{http://elibrary.ru/item.asp?id=32428047}
\transl
\jour Funct. Anal. Appl.
\yr 2018
\vol 52
\issue 1
\pages 66--69
\crossref{https://doi.org/10.1007/s10688-018-0210-y}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000428558200010}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85044715921}


Linking options:
  • http://mi.mathnet.ru/eng/faa3491
  • https://doi.org/10.4213/faa3491
  • http://mi.mathnet.ru/eng/faa/v52/i1/p80

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


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

    This publication is cited in the following articles:
    1. Rabinovich V.S. Barrera-Figueroa V. Olivera Ramirez L., “On the Spectra of One-Dimensional Schrodinger Operators With Singular Potentials”, Front. Physics, 7 (2019), 57  crossref  isi  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
    Number of views:
    This page:187
    References:37
    First page:29

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020