Sharp Li--Yau Inequalities for Dunkl Harmonic Oscillators

Abstract

We study the Li--Yau inequality for the heat equation corresponding to the Dunkl harmonic oscillator, which is a non-local Schrödinger 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.

arXiv admin note: text overlap with arXiv:2105.10132

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