On slice polyanalytic functions of a quaternionic variable

Published 17 Dec 2018 in math.CV | (1812.07018v2)

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.

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