English

The C-property for slice regular functions and applications to the Bergman space

Complex Variables 2014-06-24 v1

Abstract

This paper has a twofold purpose: on one hand we deepen the study of slice regular functions by studying their behavior with respect to the so-called C-property and anti-C-property. We show that, for any fixed basis of the algebra of quaternions H\mathbb{H} any slice regular function decomposes into the sum of four slice regular components each of them satisfying the C-property. Then, we will use these results to show a reproducing property of the Bergman kernels of the second kind.

Keywords

Cite

@article{arxiv.1406.5586,
  title  = {The C-property for slice regular functions and applications to the Bergman space},
  author = {Fabrizio Colombo and J. Oscar Gonzales-Cervantes},
  journal= {arXiv preprint arXiv:1406.5586},
  year   = {2014}
}