Abstract:
We show an approximation of Hardy function on
compact Lie groups by the methods of Bochner-Riesz
mean .We establish the Sharp Garding inequality on
compact Lie groups. The positivity condition is
expressed in the non-commutative phase space in terms
of the full matrix symbol, which is defined using the
representation of the group. Feffermanand Steinand
Lp
Waingerprovedoptimal boundedness
certainoscillating
for
multipliers on the Euclidean space.
We develop the functional calculus for elliptic operators
on compact Lie groups without the assumption that the
operator is a classical pseudo-differential operator.
Consequently, we provided asymbolic description of
.complex powers of such operators
