arXiv subjects

Michael Gilliam

Publications and source records attributed to Michael Gilliam.

2 recordsLinked to original sources

arXiv2011

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

We consider the Szegö kernel for domains Ωin C^2 given by Ω= {(z,w): Im w > b(Re z)} where b is a non-convex quartic polynomial with positive leading coefficient. Such domains are not pseudoconvex. We describe the subset of \barΩ \times \barΩ on which the kernel and all its derivatives are finite. In particular, we show that there are points off the diagonal of the boundary at which the Szegö kernel is infitie as well as points on the diagonal at which it is finite.

math.CV↗

arXiv2011

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

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.

math.CV↗