Restriction of square integrable representations: Discrete spectrum

In this paper, we study the problem of restricting a square integrable representation of a connected semisimple Lie group to a reductive subgroup. Using a geometric method of restricting sections of a vector bundle to a submanifold, we obtain information about both the discrete and the continuous spectrum. We also show the (L-2, L-2)- continuity of the associated Berezin transform and that, tinder suitable general conditions, the Berezin transform is (L-p, L-p)-continuous for 1 less than or equal to p less than or equal to infinity.