%0 Journal Article
%T The C-property for slice regular functions and applications to the Bergman space
%A Fabrizio Colombo
%A J. Oscar Gonzales-Cervantes
%J Mathematics
%D 2014
%I arXiv
%R 10.1080/17476933.2012.674521
%X 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 $\mathbb{H}$ 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.
%U http://arxiv.org/abs/1406.5586v1