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



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Izv. Akad. Nauk SSSR Ser. Mat., 1989, Volume 53, Issue 1, Pages 45–65 (Mi izv1161)  

This article is cited in 2 scientific papers (total in 2 papers)

Analytic perturbation theory for a periodic potential

Yu. E. Karpeshina


Abstract: The operator $\mathbf H_\alpha=(-\Delta)^l+\alpha V$ is considered in $L_2(\mathbf R^n)$; here $4l>n+1$, $n\geqslant2$, $V$ is a periodic potential, and $\alpha$ is a perturbation parameter, $-1\leqslant\alpha\leqslant1$. An analytic perturbation theory with respect to $\alpha$ is constructed for Block eigenfunctions and the corresponding eigenvalues of $\mathbf H_\alpha$. It is proved that, for large energies, when the quasimomentum belongs to a sufficiently rich set they admit expansion in a Taylor series in the disk $|\alpha|\leqslant1$, and these series are asymptotic in the energy and infinitely differentiable with respect to the quasimomentum.
Bibliography: 14 titles.

Full text: PDF file (1985 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1990, 34:1, 43–64

Bibliographic databases:

UDC: 517.947
MSC: 35J10, 35B20, 35P99
Received: 22.12.1986

Citation: Yu. E. Karpeshina, “Analytic perturbation theory for a periodic potential”, Izv. Akad. Nauk SSSR Ser. Mat., 53:1 (1989), 45–65; Math. USSR-Izv., 34:1 (1990), 43–64

Citation in format AMSBIB
\Bibitem{Kar89}
\by Yu.~E.~Karpeshina
\paper Analytic perturbation theory for a~periodic potential
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1989
\vol 53
\issue 1
\pages 45--65
\mathnet{http://mi.mathnet.ru/izv1161}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=992978}
\zmath{https://zbmath.org/?q=an:0689.35065}
\transl
\jour Math. USSR-Izv.
\yr 1990
\vol 34
\issue 1
\pages 43--64
\crossref{https://doi.org/10.1070/IM1990v034n01ABEH000584}


Linking options:
  • http://mi.mathnet.ru/eng/izv1161
  • http://mi.mathnet.ru/eng/izv/v53/i1/p45

    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. Yu. E. Karpeshina, “Perturbation theory formulas for the Schrödinger equation with a nonsmooth periodic potential”, Math. USSR-Sb., 71:1 (1992), 101–123  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. V. A. Geiler, V. A. Margulis, I. I. Chuchaev, “On lacunae in the spectrum of the three-dimensional periodic Schrödinger operator with a magnetic field”, Russian Math. Surveys, 50:1 (1995), 198–199  mathnet  crossref  mathscinet  zmath  adsnasa  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:246
    Full text:81
    References:40
    First page:1

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