English

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

Complex Variables 2016-01-13 v1

Abstract

In this paper we investigate the Bergman kernel function for intersection of two complex ellipsoids {(z,w1,w2)Cn+2:z12++zn2+w1q<1,z12++zn2+w2r<1}.\{(z,w_1,w_2) \in \mathbb{C}^{n+2} : |z_1|^2 + \cdots + |z_n|^2 + |w_1|^q < 1, \quad |z_1|^2 + \cdots + |z_n|^2 + |w_2|^r < 1\}.

Keywords

Cite

@article{arxiv.1601.02989,
  title  = {The Bergman kernel: explicit formulas, deflation, Lu Qi-Keng problem and Jacobi Polynomials},
  author = {Tomasz Beberok},
  journal= {arXiv preprint arXiv:1601.02989},
  year   = {2016}
}

Comments

11 pages

R2 v1 2026-06-22T12:28:04.511Z