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Fractional Multicomplex Polynomials

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In this paper we will investigate fractional analytic properties of multi-complex valued polynomials defined on \(\mathbb {BC}_n\) (the space of multicomplex numbers refers to the space generated over the reals by n commuting imaginary units) using a modification of the Cauchy–Riemann operator that substitutes the classical partial derivative for a fractional derivative.

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The authors would like to thank the reviewers for the many useful comments which lead to improvements in the paper.

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Correspondence to Antonio Di Teodoro.

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Communicated by Irene Sabadini.

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This article is part of the topical collection “Higher Dimensional Geometric Function Theory and Hypercomplex Analysis” edited by Irene Sabadini, Michael Shapiro and Daniele Struppa.

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Ceballos, J., Coloma, N., Di Teodoro, A. et al. Fractional Multicomplex Polynomials. Complex Anal. Oper. Theory 16, 60 (2022).

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