The Szegö kernel for certain non-pseudoconvex domains in C²

2011/07/08 by Michael Gilliam, Gilliam, Michael, Jennifer Halfpap +1
Mathematics · #32T99 #42B20 #Advanced Harmonic Analysis Research #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1107.1687

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 domains Ωin C² 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 Ω × Ω 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.

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