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arXiv · 2201.09981

Cauchy-Riemann operators and local slice analysis over real alternative algebras

Alessandro Perotti
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Abstract

We prove some formulas relating Cauchy-Riemann operators defined on hypercomplex subspaces of an alternative *-algebra to a differential operator associated with the concept of slice-regularity and to the spherical Dirac operator. These results in particular allow to introduce a definition of locally slice-regular function and open the path for local slice analysis. Since Cauchy-Riemann operators factor the corresponding Laplacian operators, the proven formulas let us also obtain several results about the harmonicity and polyharmonicity properties of slice-regular functions.

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Alessandro Perotti. 2022-01-24. Cauchy-Riemann operators and local slice analysis over real alternative algebras. https://doi.org/10.1016/j.jmaa.2022.126480

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