Asymptotic expansion of the Bergman kernel for weakly pseudoconvex tube domains in C^2
Abstract
In this paper we give an asymptotic expansion of the Bergman kernel for certain weakly pseudoconvex tube domains of finite type in C^2. 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 blowingup 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 1996
 DOI:
 10.48550/arXiv.math/9610201
 arXiv:
 arXiv:math/9610201
 Bibcode:
 1996math.....10201K
 Keywords:

 Mathematics  Complex Variables;
 32