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Hermite functions #18548

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thewilsonator opened this issue Nov 2, 2024 · 0 comments

thewilsonator commented Nov 2, 2024

https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Gaussian/FourierTransform.html#fourierIntegral_gaussian_pi gives the Fourier Transform of a Gaussian

https://github.com/leanprover-community/mathlib4/tree/master/Mathlib/RingTheory/Polynomial/Hermite defines the Hermite polynomials

Missing are:

Hermite functions (continuity, IsBigO, Schwartz)
their Fourier transforms as eigenfunctions and diagonalisation of the Fourier transform as an orthogonal basis of L^2(R)
Hermite polynomials as a sequence of orthogonal polynomials under the gaussian measure

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