Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2022; 59(3): 449-468

Published online May 1, 2022 https://doi.org/10.4134/JKMS.j200373

Copyright © The Korean Mathematical Society.

Zeros of new Bergman kernels

Noureddine Ghiloufi, Safa Snoun

LR17ES11 Mathematics and Applications; LR17ES11 Mathematics and Applications

Abstract

In this paper we determine explicitly the kernels $\mathbb K_{\alpha,\beta}$ associated with new Bergman spaces $\mathcal A_{\alpha,\beta}^2(\mathbb D)$ considered recently by the first author and M. Zaway. Then we study the distribution of the zeros of these kernels essentially when $\alpha\in\mathbb N$ where the zeros are given by the zeros of a real polynomial $Q_{\alpha,\beta}$. Some numerical results are given throughout the paper.

Keywords: Bergman spaces, Bergman Kernels, zeros of holomorphic functions, algebraic sets

MSC numbers: 30H20, 30C15