Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orthogonal Polynomials and Sharp Estimates for the Schr\"odinger
  Equation   In this paper we study sharp estimates for the Schr\"odinger operator via the
framework of orthogonal polynomials. We use spherical harmonics and Gegenbauer
polynomials to prove a new weighted inequality for the Schr\"odinger equation
that is maximized by radial functions. We use Hermite and Laguerre polynomial
expansions to produce sharp Strichartz estimates for even exponents. In
particular, for radial initial data in dimension 2, we establish an interesting
connection of the Strichartz norm with a combinatorial problem about words with
four letters.

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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph