Asymptotic expansion of the Bergman kernel for weakly pseudoconvex tube domains in C²

1996/10/10 by Joe Kamimoto, Kamimoto, Joe
Mathematics · #Holomorphic and Operator Theory #Algebraic and Geometric Analysis #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.math/9610201

Abstract

In this paper we give an asymptotic expansion of the Bergman kernel for certain weakly pseudoconvex tube domains of finite type in C². Our asymptotic formula asserts that the singularity of the Bergman kernel at weakly pseudoconvex points is essentially expressed by using two variables; moreover certain real blowing-up is necessary to understand its singularity. The form of the asymptotic expansion with respect to each variable is similar to that in the strictly pseudoconvex case due to C. Fefferman. We also give an analogous result in the case of the Szego kernel.

Related

• The asymptotic behavior of the Bergman kernel on pseudoconvex model domains
• Asymptotic behavior of the Bergman kernel and associated invariants in weakly pseudoconvex domains
• The Log term in the Bergman and Szeg\H o kernels in strictly pseudoconvex domains in \mathbb C²
• Singularities of the Bergman kernel for certain weakly pseudoconvex domains
• Comparison of the Bergman and Szegö kernels