Geodesic
Lagrangian Manifolds Related to the Asymptotics of Hermite Polynomials
Matematičeskie zametki, Tome 104 (2018) no. 6, pp. 835-850

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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.
Mots-clés : Hermite polynomial
Keywords: Lagrangian manifold, Maslov canonical operator, asymptotics, finite-difference equation, Schrödinger equation. 
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     author = {S. Yu. Dobrokhotov and A. V. Tsvetkova},
     title = {Lagrangian {Manifolds} {Related} to the {Asymptotics} of {Hermite} {Polynomials}},
     journal = {Matemati\v{c}eskie zametki},
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S. Yu. Dobrokhotov; A. V. Tsvetkova. Lagrangian Manifolds Related to the Asymptotics of Hermite Polynomials. Matematičeskie zametki, Tome 104 (2018) no. 6, pp. 835-850. http://geodesic.mathdoc.fr/item/MZM_2018_104_6_a3/