Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extension Properties and Boundary Estimates for a Fractional Heat
  Operator   The square root of the heat operator $\sqrt{\partial_t-\Delta}$, can be
realized as the Dirichlet to Neumann map of the heat extension of data on
$\mathbb R^{n+1}$ to $\mathbb R^{n+2}_+$. In this note we obtain similar
characterizations for general fractional powers of the heat operator,
$(\partial_t-\Delta)^s$, $s\in (0,1)$. Using the characterizations we derive
properties and boundary estimates for parabolic integro-differential equations
from purely local arguments in the extension problem.

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The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom