A Cauchy Integral Formula for Inframonogenic Functions in Clifford Analysis

In this paper we derive a Cauchy integral representation formula for the solutions of the sandwich equation ∂ x ̲ f ∂ x ̲ = 0 , where ∂ x ̲ stands for the first-order vector-valued rotation invariant differential operator in the Euclidean space R m , called Dirac operator. Such a solutions are refer...

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Veröffentlicht in:Advances in applied Clifford algebras 2017-06, Vol.27 (2), p.1147-1159
Hauptverfasser: García, Arsenio Moreno, García, Tania Moreno, Blaya, Ricardo Abreu, Reyes, Juan Bory
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Sprache:eng
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Zusammenfassung:In this paper we derive a Cauchy integral representation formula for the solutions of the sandwich equation ∂ x ̲ f ∂ x ̲ = 0 , where ∂ x ̲ stands for the first-order vector-valued rotation invariant differential operator in the Euclidean space R m , called Dirac operator. Such a solutions are referred in the literature as inframonogenic functions and represent an extension of the monogenic functions, i.e., null solutions of ∂ x ̲ , which represent higher-dimensional generalizations of the classic Cauchy–Riemann operator.
ISSN:0188-7009
1661-4909
DOI:10.1007/s00006-016-0745-z