Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classical Proofs Of Kato Type Smoothing Estimates for The Schr\"odinger
  Equation with Quadratic Potential in R^n+1 with application   This paper applies Hermite function techniques to give elementary proofs of
Kato type smoothing estimates for the Schr\"odinger equation with quadratic
potential in R^n+1. This is equivalent to proving a uniform L^2(R^n) to
L^2(R^n) boundedness for a family of singularized Hermite projection kernels.
As an applicationas the above estimate, we also prove the R^9 collapsing
variable type Strichartz estimate.

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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: econ