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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)
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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
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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