On the Π-operator in Clifford analysis

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:434

Article

Abreu Blaya, Ricardo¹  Bory Reyes, Juan²  Adan, Ali Guzman³  Kahler, Uwe⁴ 

[1] Univ Holguin, Fac Informat & Matemat, Holguin 80100, Cuba

[2] Inst Politecn Nacl, ESIME Zacatenco, Mexico City 07738, DF, Mexico

[3] Univ Ghent, Dept Math Anal, Clifford Res Grp, Fac Engn & Architecture, Galglaan 2, B-9000 Ghent, Belgium

[4] Univ Aveiro, Dept Matemat, Aveiro, Portugal

关键词: Clifford analysis;    Teodorescu transform;    Pi-operator;    Beltrami equation;   

DOI  :  10.1016/j.jmaa.2015.09.038

来源: Elsevier

【 摘 要 】

In this paper we prove that a generalization of complex Pi-operator in Clifford analysis, obtained by the use of two orthogonal bases of a Euclidean space, possesses several mapping and invertibility properties, as studied before for quaternion-valued functions as well as in the standard Clifford analysis setting. We improve and generalize most of those previous results in this direction and additionally other consequent results are presented. In particular, the expression of the jump of the generalized Pi-operator across the boundary of the domain is obtained as well as an estimate for the norm of the Pi-operator is given. At the end an application of the generalized Pi-operator to the solution of Beltrami equations is studied where we give conditions for a solution to realize a local and global homeomorphism. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free