restriction of square integrable representations:discrete spectrum

ORSTED BENT, VARGAS JORGE

DUKE MATHEMATICAL JOURNAL

duke university press

Lugar: north carolina; Año: 2004 vol. 123 p. 609 - 633

0012-7094

In this paper, we study the problem of restricting a squareintegrable representation of a connected semisimple Lie group to areductive subgroup. Using a geometric method of restrictingsections of a vector bundle to a submanifold, we obtaininformation about both the discrete and the continuous spectrum.We also show the $(L^2,L^2)-$continuity of the associated Berezintransform as well as that, under suitable general conditions, theBerezin transform is $(L^p, L^p)-$continuous for $ 1 \leq p \leq\infty.$