Quantization of bounded domains

We consider the quantization of a complex manifold endowed with the Bergman form following the ideas of Cahen, Gutt and Rawnsley. In particular we giv e a geometric interpretation for the quantization to be regular in terms of the Hilbert space of square integrable holomorphic n-forms on M and the Hi lbert space of holomorphic n-forms on M bounded with respect to the Liouvil le element. (C) 1999 Published by Elsevier Science B.V. All rights reserved .