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 |
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Hauptverfasser: | , , , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
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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. |
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ISSN: | 0188-7009 1661-4909 |
DOI: | 10.1007/s00006-016-0745-z |