Higher order Borel–Pompeiu representations in Clifford analysis

Juan Bory Reyes; Hennie De Schepper; Alí Guzmán Adán; Frank Sommen

doi:10.1002/mma.3798

Higher order Borel–Pompeiu representations in Clifford analysis

Juan Bory Reyes, Hennie De Schepper, Alí Guzmán Adán, Frank Sommen

Escuela Superior de Ingeniería Mecánica y Eléctrica (ESIME), Unidad Zacatenco

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	4787-4796
Number of pages	10
Journal	Mathematical Methods in the Applied Sciences
Volume	39
Issue number	16
DOIs	https://doi.org/10.1002/mma.3798
State	Published - 15 Nov 2016

Keywords

31B10
32A26
Borel–Pompeiu representation
Cauchy–Riemann operator
Clifford analysis
higher order Cauchy–type integral
higher order Téodorescu transform
structural set
subclass 30G35

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10.1002/mma.3798

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title = "Higher order Borel–Pompeiu representations in Clifford analysis",

abstract = "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.",

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author = "Reyes, {Juan Bory} and Schepper, {Hennie De} and Ad{\'a}n, {Al{\'i} Guzm{\'a}n} and Frank Sommen",

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AU - Reyes, Juan Bory

AU - Schepper, Hennie De

AU - Adán, Alí Guzmán

AU - Sommen, Frank

PY - 2016/11/15

Y1 - 2016/11/15

N2 - 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.

AB - 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.

KW - 31B10

KW - 32A26

KW - Borel–Pompeiu representation

KW - Cauchy–Riemann operator

KW - Clifford analysis

KW - higher order Cauchy–type integral

KW - higher order Téodorescu transform

KW - structural set

KW - subclass 30G35

UR - http://www.scopus.com/inward/record.url?scp=84949972261&partnerID=8YFLogxK

U2 - 10.1002/mma.3798

DO - 10.1002/mma.3798

M3 - Artículo

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VL - 39

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EP - 4796

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 16

ER -

Higher order Borel–Pompeiu representations in Clifford analysis

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Keywords

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