Matematicheskie Zametki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
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

Matematicheskie Zametki, 2018, Volume 104, Issue 6, Pages 835–850
DOI: https://doi.org/10.4213/mzm12093 (Mi mzm12093) 		 
This article is cited in 14 scientific papers (total in 14 papers)

Lagrangian Manifolds Related to the Asymptotics of Hermite Polynomials

S. Yu. Dobrokhotovab, A. V. Tsvetkovaab

a Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow
b Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
Full-text PDF (623 kB) Citations (14)
References:
PDF
HTML
DOI: https://doi.org/10.4213/mzm12093
Abstract: We discuss two approaches that can be used to obtain the asymptotics of Hermite polynomials. The first, well-known approach is based on the representation of Hermite polynomials as solutions of a spectral problem for the harmonic oscillator Schrödinger equation. The second approach is based on a reduction of the finite-difference equation for the Hermite polynomials to a pseudodifferential equation. Associated with each of the approaches are Lagrangian manifolds that give the asymptotics of Hermite polynomials via the Maslov canonical operator.
Keywords: Hermite polynomial, Lagrangian manifold, Maslov canonical operator, asymptotics, finite-difference equation, Schrödinger equation.
Funding agency Grant number
Russian Science Foundation 16-11-10282
This work was supported by the Russian Science Foundation under grant 16-11-10282.
Received: 14.06.2018
English version:
Mathematical Notes, 2018, Volume 104, Issue 6, Pages 810–822
DOI: https://doi.org/10.1134/S0001434618110263
Bibliographic databases:
Document Type: Article
UDC: 517.928
Language: Russian
Citation: S. Yu. Dobrokhotov, A. V. Tsvetkova, “Lagrangian Manifolds Related to the Asymptotics of Hermite Polynomials”, Mat. Zametki, 104:6 (2018), 835–850; Math. Notes, 104:6 (2018), 810–822
Citation in format AMSBIB
\Bibitem{DobTsv18}
\by S.~Yu.~Dobrokhotov, A.~V.~Tsvetkova
\paper Lagrangian Manifolds Related to the Asymptotics of Hermite Polynomials
\jour Mat. Zametki
\yr 2018
\vol 104
\issue 6
\pages 835--850
\mathnet{http://mi.mathnet.ru/mzm12093}
\crossref{https://doi.org/10.4213/mzm12093}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3881775}
\elib{https://elibrary.ru/item.asp?id=36448723}
\transl
\jour Math. Notes
\yr 2018
\vol 104
\issue 6
\pages 810--822
\crossref{https://doi.org/10.1134/S0001434618110263}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000454546800026}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85059235880}
Linking options:
  • https://www.mathnet.ru/eng/mzm12093
  • https://doi.org/10.4213/mzm12093
  • https://www.mathnet.ru/eng/mzm/v104/i6/p835
    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
    Statistics & downloads:
    Abstract page:474
    Full-text PDF :82
    References:77
    First page:22
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024