Sharp Garding inequality on compact Lie groups

TL;DR

This paper extends the sharp Garding inequality to compact Lie groups, providing a non-commutative phase space framework and applications to boundedness of pseudo-differential operators.

Contribution

It introduces a new formulation of the positivity condition in the non-commutative phase space using group representations, advancing analysis on compact Lie groups.

Findings

Establishment of the sharp Garding inequality on compact Lie groups

Characterization of positivity in the non-commutative phase space

Applications to $L^2$ and Sobolev boundedness of pseudo-differential operators

Abstract

In this paper the sharp Garding inequality is established on compact Lie groups. The positivity condition is expressed in the non-commutative phase space in terms of the full symbol, which is defined using the representations of the group. Applications are given to the $L^2$ and Sobolev boundedness of pseudo-differential operators.