Lagrangian Manifolds Related to the Asymptotics of Hermite Polynomials
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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.
KeywordsHermite polynomial Lagrangian manifold Maslov canonical operator asymptotics finite-difference equation Schrödinger equation
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