Email this article Lagrangian Manifolds Related to the Asymptotics of Hermite Polynomials
- Authors: Dobrokhotov S.Y.1,2, Tsvetkova A.V.1,2
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Affiliations:
- Ishlinsky Institute for Problems in Mechanics RAS
- Moscow Institute of Physics and Technology (State University)
- Issue: Vol 104, No 5-6 (2018)
- Pages: 810-822
- Section: Article
- URL: https://ogarev-online.ru/0001-4346/article/view/150441
- DOI: https://doi.org/10.1134/S0001434618110263
- ID: 150441
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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.
About the authors
S. Yu. Dobrokhotov
Ishlinsky Institute for Problems in Mechanics RAS; Moscow Institute of Physics and Technology (State University)
Author for correspondence.
Email: dobr@ipmnet.ru
Russian Federation, Moscow, 119526; Dolgoprudny, Moscow Oblast, 141701
A. V. Tsvetkova
Ishlinsky Institute for Problems in Mechanics RAS; Moscow Institute of Physics and Technology (State University)
Email: dobr@ipmnet.ru
Russian Federation, Moscow, 119526; Dolgoprudny, Moscow Oblast, 141701
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