The Bergman kernel on certain decoupled domains (Q2712250)

This paper studies the singularities of the Bergman and Szegő kernel functions of the decoupled tube domains of finite type of the special form \(\{ z\in\mathbb{C}^{n+1}: \Im z_{n+1} > \sum_{j=1}^n a_j (\Im z_j)^{2m_j} \}\), where the \(a_j\) are positive real numbers and the \(m_j\) are positive integers not all equal to~\(1\). To characterize the singularity on the diagonal near a weakly pseudoconvex boundary point, the author introduces new coordinates by blowing up at the point. To understand the singularity off the diagonal, the author represents the singularity as a superposition of countably many functions whose singularities can be understood concretely.NEWLINENEWLINEFor the entire collection see [Zbl 0957.00034].