English

Vanishing Bergman kernels on the disk

Complex Variables 2017-03-20 v1

Abstract

We discuss topics related to zeroes of the Bergman kernels, and present a method for generating Bergman kernels with arbitrarily, but finitely, many zeroes. It is also shown that a Bergman kernel induced by a radial weight on the unit disk cannot have infinitely many zeroes. Similar questions for the Segal-Bargmann spaces of the complex plane are briefly discussed.

Keywords

Cite

@article{arxiv.1703.05976,
  title  = {Vanishing Bergman kernels on the disk},
  author = {Antti Perälä},
  journal= {arXiv preprint arXiv:1703.05976},
  year   = {2017}
}

Comments

11 pages

R2 v1 2026-06-22T18:48:42.515Z