Asymptotic expansion of the Bergman kernel for strictly pseudoconvex complete Reinhardt domains in \(\mathbb{C}^ 2\)
type: Item
instance of: scholarly article
title: Asymptotic expansion of the Bergman kernel for strictly pseudoconvex complete Reinhardt domains in \(\mathbb{C}^ 2\)
zbMATH Open document ID: 0818.32001
author: Noriyuki Nakazawa
published in: Osaka Journal of Mathematics
publication date: 1995-08-15T00:00:00Z
review text: \textit{C. Fefferman} [Invent. Math. 26, 1-65 (1974; Zbl 0289.32012)] has studied asymptotic expansion of the Bergman kernel for a strictly pseudoconvex domain. This paper concerns the class of strictly pseudo- convex, complete Reinhardt domains in \(\mathbb{C}^ 2\) and presents an integral representation of the symbol of a pseudodifferential operator which represents the singularity of the Bergman kernel. By using that integral representation, the author identifies the first six coefficients of Fefferman's asymptotic expansion. There is also a formula that would allow, in principle, to compute all the coefficients \(L_ n\). In view of the many pages of complicated calculations involved in order to get \(L_ n\), \(n \leq 5\), this would appear to be very difficult.
Mathematics Subject Classification ID: 32A07
Mathematics Subject Classification ID: 32A25
zbMATH DE Number: 720166
zbMATH Keywords: Bergman kernel
zbMATH Keywords: strictly pseudoconvex
zbMATH Keywords: Reinhardt domains
zbMATH Keywords: integral representation
zbMATH Keywords: Fefferman's asymptotic expansion
reviewed by: Edwin J. Akutowicz
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 720166