Bergman spaces of naturalG-manifolds.
LetGbe a unimodular Lie group,Xa compact manifold with boundary, andMthe total space of a principal bundle [Formula: see text] so thatMis also a strongly pseudoconvex complex manifold. In this work, we show that if there exists a point [Formula: see text] such that [Formula: see text] is contained in the complex tangent space [Formula: see text] ofbMatp, then the Bergman space ofMis large. Natural examples include the gaugedG-complexifications of Heinzner, Huckleberry, and Kutzschebauch.
Fakultät für Mathematik, Universität Wien, Vienna, Austria.
Giuseppe
G
Della Sala
Joe J
JJ
Perez
Bergman space; Free actions of Lie groups; Holomorphic peak functions; Representation of unimodular Lie groups