On slice polyanalytic functions of a quaternionic variable

Abstract

In this paper, we introduce the quaternionic slice polyanalytic functions and we prove some of their properties. Then, we apply the obtained results to begin the study of the quaternionic Fock and Bergman spaces in this new setting. In particular, we give explicit expressions of their reproducing kernels.

A Corrigendum to the previous version is contained at the end of the paper