The best I could find on the net is this paper, http://arxiv.org/pdf/math/0401310.pdf
Has this been improved?
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Sign up to join this communityThe best I could find on the net is this paper, http://arxiv.org/pdf/math/0401310.pdf
Has this been improved?
Not a comprehensive answer, but this paper contains some pointwise bounds on Hermite polynomials. It seems that it gives a different flavour of the $L^{\infty}$ bound by splitting it to $\mathbb{R}$ bounds and "central" bounds.
Also, for what it's worth, it seems that no one who's citing the aforementioned paper has a better bound.