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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



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






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


Mat. Zametki, 2003, Volume 73, Issue 1, Pages 49–62 (Mi mz167)  

This article is cited in 9 scientific papers (total in 9 papers)

Absolute Continuity of the Spectrum of a Periodic Schrödinger Operator

L. I. Danilov

Physical-Technical Institute of the Ural Branch of the Russian Academy of Sciences

Abstract: We prove the absolute continuity of the spectrum of the Schrödinger operator in $L^2(\mathbb R^n)$, $n\ge3$, with periodic (with a common period lattice $\Lambda$) scalar $V$ and vector $A\in C^1(\mathbb R^n,\mathbb R^n)$ potentials for which either $A\in H_{\operatorname{loc}}^q(\mathbb R^n;\mathbb R^n)$, $2q>n-2$, or the Fourier series of the vector potential $A$ converges absolutely, $V\in L_w^{p(n)}(K)$, where $K$ is an elementary cell of the lattice $\Lambda$, $p(n)=n/2$ for $n=3,4,5,6$, and $p(n)=n-3$ for $n\ge7$, and the value of $\lim_{t\to+\infty}\|\theta_tV\|_{L_w^{p(n)}(K)}$ is sufficiently small, where $\theta_t(x)=0$, if $|V(x)|\le t$ and $\theta_t(x)=1$ otherwise, $x\in K$ and $t>0$.

DOI: https://doi.org/10.4213/mzm167

Full text: PDF file (274 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2003, 73:1, 46–57

Bibliographic databases:

UDC: 517.9
Received: 28.07.2000

Citation: L. I. Danilov, “Absolute Continuity of the Spectrum of a Periodic Schrödinger Operator”, Mat. Zametki, 73:1 (2003), 49–62; Math. Notes, 73:1 (2003), 46–57

Citation in format AMSBIB
\Bibitem{Dan03}
\by L.~I.~Danilov
\paper Absolute Continuity of the Spectrum of a Periodic Schr\"odinger Operator
\jour Mat. Zametki
\yr 2003
\vol 73
\issue 1
\pages 49--62
\mathnet{http://mi.mathnet.ru/mz167}
\crossref{https://doi.org/10.4213/mzm167}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1993539}
\zmath{https://zbmath.org/?q=an:1163.35443}
\transl
\jour Math. Notes
\yr 2003
\vol 73
\issue 1
\pages 46--57
\crossref{https://doi.org/10.1023/A:1022169916738}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000181384200005}


Linking options:
  • http://mi.mathnet.ru/eng/mz167
  • https://doi.org/10.4213/mzm167
  • http://mi.mathnet.ru/eng/mz/v73/i1/p49

    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. L. I. Danilov, “The Spectrum of the Two-Dimensional Periodic Schrödinger Operator”, Theoret. and Math. Phys., 134:3 (2003), 392–403  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. L. I. Danilov, “The absence of eigenvalues in the spectrum of ageneralized two-dimensional periodic Dirac operator”, St. Petersburg Math. J., 17:3 (2006), 409–433  mathnet  crossref  mathscinet  zmath
    3. L. I. Danilov, “Ob absolyutnoi nepreryvnosti spektra trekhmernogo periodicheskogo operatora Diraka”, Izv. IMI UdGU, 2006, no. 1(35), 49–76  mathnet
    4. Shen, ZW, “Uniform Sobolev inequalities and absolute continuity of periodic operators”, Transactions of the American Mathematical Society, 360:4 (2008), 1741  crossref  mathscinet  zmath  isi  scopus  scopus
    5. Danilov, LI, “On absolute continuity of the spectrum of a periodic magnetic Schrodinger operator”, Journal of Physics A-Mathematical and Theoretical, 42:27 (2009), 275204  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    6. Danilov L.I., “On absolute continuity of the spectrum of three- and four-dimensional periodic Schrodinger operators”, Journal of Physics A-Mathematical and Theoretical, 43:21 (2010), 215201  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    7. Danilov L.I., “On Absolute Continuity of the Spectrum of a 3D Periodic Magnetic Dirac Operator”, Integr. Equ. Oper. Theory, 71:4 (2011), 535–556  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    8. L. I. Danilov, “O spektre periodicheskogo operatora Shredingera s potentsialom iz prostranstva Morri”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2012, no. 3, 25–47  mathnet
    9. Kuchment P., “An overview of periodic elliptic operators”, Bull. Amer. Math. Soc., 53:3 (2016), 343–414  crossref  mathscinet  zmath  isi  elib  scopus
  • Математические заметки Mathematical Notes
    Number of views:
    This page:410
    Full text:64
    References:46
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019