Abstract

We establish a subelliptic sharp Gårding inequality on compact Lie groups for pseudodifferential operators with symbols belonging to global subelliptic Hörmander classes. In order for the inequality to hold we require the global matrix-valued symbol to satisfy the suitable classical nonnegativity condition in our setting. Our result extends to ${\mathcal{𝒮}}_{\rho ,\delta }^m(G)$-classes, $0\le \delta <\rho$, the one of Ruzhansky and Turunen (2011) about the validity of the sharp Gårding inequality for the class ${\mathcal{𝒮}}_{1,0}^m(G)$. We remark that the result we prove here is already new and sharp in the case of the torus.

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