In this paper we study the additive splitting associated to the quaternionic Cauchy transform defined by the Cauchy formula of slice hyperholomorphic functions. Moreover, we introduce and study the analogue of the fundamental solution of the global operator of slice hyperholomorphic functions. We state our results in the quaternionic setting but several results hold for Clifford algebra-valued function with minor changes in the proofs.

The Cauchy transform in the slice hyperholomorphic setting and related topics

Colombo, Fabrizio;Mongodi, Samuele
2019-01-01

Abstract

In this paper we study the additive splitting associated to the quaternionic Cauchy transform defined by the Cauchy formula of slice hyperholomorphic functions. Moreover, we introduce and study the analogue of the fundamental solution of the global operator of slice hyperholomorphic functions. We state our results in the quaternionic setting but several results hold for Clifford algebra-valued function with minor changes in the proofs.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1071591
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