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 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}
}