Weighted parameter dependent Bergman kernel, Bergman projection and Fourier integral operators
This article is motivated by a theorem of \textit{D.~Catlin} [Komatsu, Gen (ed.) et al., Analysis and geometry in several complex variables. Proceedings of the 40th Taniguchi symposium, Katata, Japan, June 23--28, 1997. Boston, MA: Birkhäuser. Trends in Mathematics. 1--23 (1999; Zbl 0941.32002)], according to which the Bergman kernel of the projection onto the square-integrable holomorphic sections of a holomorphic vector bundle over a smoothly bounded strictly pseudoconvex manifold is a Fourier integral operator. The authors generalize to the case of a weighted Bergman kernel depending on parameters.
scientific article; zbMATH DE number 5635209