Jump problem and removable singularities for monogenic functions

Ricardo Abreu-Blaya; Juan Bory-Reyes; Dixan Peña-Peña

doi:10.1007/BF02922079

Jump problem and removable singularities for monogenic functions

Ricardo Abreu-Blaya, Juan Bory-Reyes, Dixan Peña-Peña

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

47 Scopus citations

Abstract

In this article the jump problem for monogenic functions (Clifford holomorphicity) on the boundary of a Jordan domain in Euclidean spaces is investigated. We shall establish some criteria that imply the uniqueness of the solution in terms of a natural analogue of removable singularities in the plane to R ⁿ⁺¹ (n ≥ 2). Sufficient conditions to extend monogenically continuous Clifford algebra valued functions across a hypersurface are proved.

Original language	English
Pages (from-to)	1-13
Number of pages	13
Journal	Journal of Geometric Analysis
Volume	17
Issue number	1
DOIs	https://doi.org/10.1007/BF02922079
State	Published - 2007
Externally published	Yes

Keywords

Canchy transform
Clifford analysis
removable singularities

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10.1007/BF02922079

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title = "Jump problem and removable singularities for monogenic functions",

abstract = "In this article the jump problem for monogenic functions (Clifford holomorphicity) on the boundary of a Jordan domain in Euclidean spaces is investigated. We shall establish some criteria that imply the uniqueness of the solution in terms of a natural analogue of removable singularities in the plane to R n+1 (n ≥ 2). Sufficient conditions to extend monogenically continuous Clifford algebra valued functions across a hypersurface are proved.",

keywords = "Canchy transform, Clifford analysis, removable singularities",

author = "Ricardo Abreu-Blaya and Juan Bory-Reyes and Dixan Pe{\~n}a-Pe{\~n}a",

note = "Funding Information: The research carried out in this article was initiated while the third author was visiting the Department of Mathematics, Universidad de Oriente, Santiago de Cuba. It was completed during his stay as a PhD-student at the Department of Mathematical Analysis, Clifford Research Group, Ghent University, supported by a Doctoral Grant of the Special Research Fund of Ghent University. He would like to express his sincere gratitude.",

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T1 - Jump problem and removable singularities for monogenic functions

AU - Abreu-Blaya, Ricardo

AU - Bory-Reyes, Juan

AU - Peña-Peña, Dixan

N1 - Funding Information: The research carried out in this article was initiated while the third author was visiting the Department of Mathematics, Universidad de Oriente, Santiago de Cuba. It was completed during his stay as a PhD-student at the Department of Mathematical Analysis, Clifford Research Group, Ghent University, supported by a Doctoral Grant of the Special Research Fund of Ghent University. He would like to express his sincere gratitude.

PY - 2007

Y1 - 2007

N2 - In this article the jump problem for monogenic functions (Clifford holomorphicity) on the boundary of a Jordan domain in Euclidean spaces is investigated. We shall establish some criteria that imply the uniqueness of the solution in terms of a natural analogue of removable singularities in the plane to R n+1 (n ≥ 2). Sufficient conditions to extend monogenically continuous Clifford algebra valued functions across a hypersurface are proved.

AB - In this article the jump problem for monogenic functions (Clifford holomorphicity) on the boundary of a Jordan domain in Euclidean spaces is investigated. We shall establish some criteria that imply the uniqueness of the solution in terms of a natural analogue of removable singularities in the plane to R n+1 (n ≥ 2). Sufficient conditions to extend monogenically continuous Clifford algebra valued functions across a hypersurface are proved.

KW - Canchy transform

KW - Clifford analysis

KW - removable singularities

UR - http://www.scopus.com/inward/record.url?scp=34147097391&partnerID=8YFLogxK

U2 - 10.1007/BF02922079

DO - 10.1007/BF02922079

M3 - Artículo

SN - 1050-6926

VL - 17

SP - 1

EP - 13

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 1

ER -

Jump problem and removable singularities for monogenic functions

Abstract

Keywords

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