The Szegö kernel for non-pseudoconvex tube domains in C^2

Abstract

We consider the Szegö kernel for non-pseudoconvex domains in C^2 given by Ω= {(z,w): Im w > b(Re z)} for b a non-convex even-degree polynomial with positive leading coefficient. This is an extension of results previously obtained by the authors for the case in which b has degree 4. We show that the Szegö kernel has singularities off the diagonal of the boundary of \barΩ \times \barΩ for all such domains, as well as points on the diagonal of the boundary at which it is finite.

17 pages