Sharp Garding inequality on compact Lie groups

Michael Ruzhansky, Ville Turunen

Published 2010-07-04, updated 2011-02-17Version 2

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.