Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hermite polynomials, linear flows on the torus, and an uncertainty
  principle for roots   We study a recent result of Bourgain, Clozel and Kahane, a version of which
states that a sufficiently nice function $f:\mathbb{R} \rightarrow \mathbb{R}$
that coincides with its Fourier transform and vanishes at the origin has a root
in the interval $(c, \infty)$, where the optimal $c$ satisfies $0.41 \leq c
\leq 0.64$. A similar result holds in higher dimensions. We improve the
one-dimensional result to $0.45 \leq c \leq 0.594$, and the lower bound in
higher dimensions. We also prove that extremizers exist, and have infinitely
many double roots. With this purpose in mind, we establish a new structure
statement about Hermite polynomials which relates their pointwise evaluation to
linear flows on the torus, and applies to other families of orthogonal
polynomials as well.

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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio
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The categories of this paper are: eess