The Szegö kernel for non-pseudoconvex tube domains in C²

2011/07/08 by Michael Gilliam, Gilliam, Michael, Jennifer Halfpap +1
Mathematics · #32T99 #42B20 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1107.1694

openalex publication_date 2011/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Szegö kernel for non-pseudoconvex domains in C² 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 Ω × Ω for all such domains, as well as points on the diagonal of the boundary at which it is finite.

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