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.

Cauchy-Riemann operators and local slice analysis over real alternative algebras / Perotti, Alessandro. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 2022:516(2022), pp. 12648001-12648034. [10.1016/j.jmaa.2022.126480]

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

Perotti, Alessandro
2022

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.
516
Perotti, Alessandro
Cauchy-Riemann operators and local slice analysis over real alternative algebras / Perotti, Alessandro. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 2022:516(2022), pp. 12648001-12648034. [10.1016/j.jmaa.2022.126480]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/329312
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