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Higher order Borel–Pompeiu representations in Clifford analysis
Author(s) -
Reyes Juan Bory,
Schepper Hennie De,
Adán Alí Guzmán,
Sommen Frank
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3798
Subject(s) - mathematics , euclidean space , clifford analysis , cauchy distribution , order (exchange) , euclidean geometry , kernel (algebra) , clifford algebra , pure mathematics , set (abstract data type) , orthogonal basis , algebra over a field , mathematical analysis , dirac operator , computer science , geometry , programming language , economics , finance , physics , quantum mechanics
In this paper, we show that a higher order Borel–Pompeiu (Cauchy–Pompeiu) formula, associated with an arbitrary orthogonal basis (called structural set) of a Euclidean space, can be extended to the framework of generalized Clifford analysis. Furthermore, in lower dimensional cases, as well as for combinations of standard structural sets, explicit expressions of the kernel functions are derived. Copyright © 2015 John Wiley & Sons, Ltd.