Minkowski Dimension and Cauchy Transform in Clifford Analysis

2007 ◽  
Vol 1 (3) ◽  
pp. 301-305 ◽  
Author(s):  
Ricardo Abreu Blaya ◽  
Juan Bory Reyes ◽  
Tania Moreno García
Keyword(s):  
Clifford Analysis ◽  
Cauchy Transform ◽  
Minkowski Dimension

The Cauchy Transform for the Hodge/De Rham System and Some of its Properties

2007 ◽  
Vol 14 (1) ◽  
pp. 1-20
Author(s):  
Ricardo Abreu-Blaya ◽  
Juan Bory-Reyes ◽  
Michael Shapiro
Keyword(s):  
Clifford Analysis ◽  
Regularity Condition ◽  
Integral Formula ◽  
Close Relation ◽  
Cauchy Transform ◽  
Necessary And Sufficient Condition ◽  
Cauchy Integral ◽  
Hyperholomorphic Functions ◽  
De Rham ◽  
Necessary And Sufficient

Abstract We study the analogue of the Cauchy transform for the theory of solutions of the Hodge/de Rham system in the case of a rectifiable surface of integration which additionally satisfies an Ahlfors/David regularity condition and we prove the Cauchy integral formula, the Plemelj/Privalov theorem and the Sokhotski/Plemelj theorem for it, as well as the necessary and sufficient condition for the possibility to extend a given 𝑘-form from such a surface to a harmonic 𝑘-form in the domain. A formula for the square of the singular Cauchy transform is given. The proofs of all these facts are based on a close relation between algebra-valued null-solutions of the Dirac operator in the Euclidean space and hyperholomorphic functions of Clifford analysis.

scholarly journals Cauchy transform on nonrectifiable surfaces in Clifford analysis

2008 ◽  
Vol 339 (1) ◽  
pp. 31-44 ◽  
Author(s):  
R. Abreu-Blaya ◽  
J. Bory-Reyes ◽  
T. Moreno-García
Keyword(s):  
Clifford Analysis ◽  
Cauchy Transform

scholarly journals Numerical Clifford analysis for nonlinear Schrödinger problem

2008 ◽  
Vol 24 (4) ◽  
pp. 1181-1202 ◽  
Author(s):  
P. Cerejeiras ◽  
N. Faustino ◽  
N. Vieira
Keyword(s):  
Clifford Analysis ◽  
Nonlinear Schrödinger

The Hermitian Clifford Analysis Toolbox

2008 ◽  
Vol 18 (3-4) ◽  
pp. 451-487 ◽  
Author(s):  
Fred Brackx ◽  
Hennie De Schepper ◽  
Frank Sommen
Keyword(s):  
Clifford Analysis ◽  
Hermitian Clifford Analysis
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