On slice polyanalytic functions of a quaternionic variable

Daniel Alpay; Kamal Diki; Irene Sabadini

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arXiv · 1812.07018

On slice polyanalytic functions of a quaternionic variable

Daniel Alpay·Kamal Diki·Irene Sabadini

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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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Daniel Alpay, Kamal Diki, Irene Sabadini. 2018-12-17. On slice polyanalytic functions of a quaternionic variable. https://arxiv.org/abs/1812.07018

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