The Szeg\"o kernel for non-pseudoconvex tube domains in C^2

Abstract

We consider the Szeg\"o kernel for non-pseudoconvex domains in C^2 given by \Omega = {(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 Szeg\"o kernel has singularities off the diagonal of the boundary of \bar{\Omega} \times \bar{\Omega} for all such domains, as well as points on the diagonal of the boundary at which it is finite.