Weighted parameter dependent Bergman kernel, Bergman projection and Fourier integral operators
type: Item
instance of: scholarly article
title: Weighted parameter dependent Bergman kernel, Bergman projection and Fourier integral operators
zbMATH Open document ID: 1193.32005
author: S. M. Einstein-Matthews
author: Jeffery S. Fleming
published in: African Diaspora Journal of Mathematics
publication date: 2009-11-18T00:00:00Z
review text: 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.
reviewed by: Harold P. Boas
Mathematics Subject Classification ID: 32A25
Mathematics Subject Classification ID: 32Q15
Mathematics Subject Classification ID: 58J40
zbMATH DE Number: 5635209
zbMATH Keywords: Bergman kernel
zbMATH Keywords: Fourier integral operator
zbMATH Keywords: Kähler manifold
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5635209