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., 2017, Volume 51, Issue 1, Pages 82–98 (Mi faa3264)  

This article is cited in 4 scientific papers (total in 4 papers)

Spectral Properties of the Complex Airy Operator on the Half-Line

A. M. Savchuk, A. A. Shkalikov

Lomonosov Moscow State University

Abstract: We prove a theorem on the completeness of the system of root functions of the Schrödinger operator $L=-d^2/dx^2 +p(x)$ on the half-line $\mathbb R_+$ with a potential $p$ for which $L$ appears to be maximal sectorial. An application of this theorem to the complex Airy operator $\mathcal L_c = - d^2/dx^2 +cx$, $c=\operatorname{const}$, implies the completeness of the system of eigenfunctions of $\mathcal L_c$ for the case in which $|\arg c| < 2\pi/3$. We use subtler methods to prove a theorem stating that the system of eigenfunctions of this special operator remains complete under the condition that $|\arg c| < 5\pi/6$.

Keywords: Schrödinger operator, complex Airy operator, nonself-adjoint operator, completeness of the eigenfunctions of a differential operator

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00706


DOI: https://doi.org/10.4213/faa3264

Full text: PDF file (268 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Functional Analysis and Its Applications, 2017, 51:1, 66–79

Bibliographic databases:

UDC: 517.984
Received: 22.12.2016
Accepted:24.01.2017

Citation: A. M. Savchuk, A. A. Shkalikov, “Spectral Properties of the Complex Airy Operator on the Half-Line”, Funktsional. Anal. i Prilozhen., 51:1 (2017), 82–98; Funct. Anal. Appl., 51:1 (2017), 66–79

Citation in format AMSBIB
\Bibitem{SavShk17}
\by A.~M.~Savchuk, A.~A.~Shkalikov
\paper Spectral Properties of the Complex Airy Operator on the Half-Line
\jour Funktsional. Anal. i Prilozhen.
\yr 2017
\vol 51
\issue 1
\pages 82--98
\mathnet{http://mi.mathnet.ru/faa3264}
\crossref{https://doi.org/10.4213/faa3264}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3647783}
\elib{http://elibrary.ru/item.asp?id=28169177}
\transl
\jour Funct. Anal. Appl.
\yr 2017
\vol 51
\issue 1
\pages 66--79
\crossref{https://doi.org/10.1007/s10688-017-0168-1}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000396373700005}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85015621792}


Linking options:
  • http://mi.mathnet.ru/eng/faa3264
  • https://doi.org/10.4213/faa3264
  • http://mi.mathnet.ru/eng/faa/v51/i1/p82

    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. Kh. K. Ishkin, “Conditions of spectrum localization for operators not close to self-adjoint operators”, Dokl. Math., 97:2 (2018), 170–173  mathnet  crossref  crossref  zmath  isi  elib  scopus
    2. I. M. Guseinov, A. Kh. Khanmamedov, A. F. Mamedova, “Inverse scattering problem for the Schrödinger equation with an additional quadratic potential on the entire axis”, Theoret. and Math. Phys., 195:1 (2018), 538–547  mathnet  crossref  crossref  adsnasa  isi  elib
    3. M. G. Mahmudova, A. Kh. Khanmamedov, “On an inverse spectral problem for a perturbed harmonic oscillator”, Azerb. J. Math., 8:2 (2018), 181–191  mathscinet  zmath  isi
    4. S. M. Bagirova, A. Kh. Khanmamedov, “The inverse spectral problem for the perturbed harmonic oscillator on the entire axis”, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb., 44:2 (2018), 285–294  mathscinet  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
    Number of views:
    This page:421
    References:69
    First page:60

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