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arXiv · 2303.11524

Sharp Li--Yau Inequalities for Dunkl Harmonic Oscillators

Huaiqian Li·Bin Qian
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Abstract

We study the Li--Yau inequality for the heat equation corresponding to the Dunkl harmonic oscillator, which is a non-local Schr\"{o}dinger operator parameterized by reflections and multiplicity functions. In the particular case when the reflection group is isomorphic to $\mathbb{Z}_2^d$, the result is sharp in the sense that equality is achieved by the heat kernel of the classic harmonic oscillator. We also provide the application on parabolic Harnack inequalities.

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Huaiqian Li, Bin Qian. 2023-03-21. Sharp Li--Yau Inequalities for Dunkl Harmonic Oscillators. https://doi.org/10.1515/forum-2022-0223

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