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In this paper, we prove that slice polyanalytic functions on quaternions can be considered as solutions of a power of some special global operator with nonconstant coefficients as it happens in the case of slice hyperholomorphic functions. We investigate also an extension version of the Fueter mapping theorem in this polyanalytic setting. In particular, we show that under axially symmetric conditions it is always possible to construct Fueter regular and poly-Fueter regular functions through slice polyanalytic ones using what we call the poly-Fueter mappings. We study also some integral representations of these results on the quaternionic unit ball.


This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Analysis and Applications, volume 19, issue 6, in 2020 following peer review. The definitive publisher-authenticated version is available online at

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World Scientific Publishing



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