The Bergman kernel: explicit formulas, deflation, Lu Qi-Keng problem and Jacobi Polynomials

Abstract

In this paper we investigate the Bergman kernel function for intersection of two complex ellipsoids $\{(z,w_1,w_2)\in {\mathbb{C}}^{n+2}:|z_1{|}^2+\cdots +|z_n{|}^2+|w_1{|}^q<1,|z_1{|}^2+\cdots +|z_n{|}^2+|w_2{|}^r<1\}.$

arXiv comment11 pages