Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Li-Yau and Harnack inequalities via curvature-dimension conditions for
  discrete long-range jump operators including the fractional discrete
  Laplacian   We consider operators of the form $L u(x) = \sum_{y \in \mathbb{Z}} k(x-y)
\big( u(y) - u(x)\big)$ on the one-dimensional lattice with symmetric,
integrable kernel $k$. We prove several results stating that under certain
conditions on the kernel the operator $L$ satisfies the curvature-dimension
condition $CD_\Upsilon (0,F)$ (recently introduced by two of the authors) with
some $CD$-function $F$, where attention is also paid to the asymptotic
properties of $F$ (exponential growth at infinity and power-type behaviour near
zero). We show that $CD_\Upsilon (0,F)$ implies a Li-Yau inequality for
positive solutions of the heat equation associated with the operator $L$. The
Li-Yau estimate in turn leads to a Harnack inequality, from which we also
derive heat kernel bounds. Our results apply to a wide class of operators
including the fractional discrete Laplacian.

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The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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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: nlin