| Autor: |
Kräss, Sebastian, Weber, Frederic, Zacher, Rico |
| Předmět: |
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| Zdroj: |
Discrete & Continuous Dynamical Systems: Series A; Jul2024, Vol. 44 Issue 7, p1-47, 47p |
| Abstrakt: |
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 the last two 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. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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