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Title: On the Π-operator in Clifford analysis
Author: Blaya, Ricardo Abreu
Reyes, Juan Bory
Adán, Alí Guzmán
Kähler, Uwe
Keywords: Clifford analysis
Teodorescu transform
Integral representations
Issue Date: 15-Feb-2016
Publisher: Elsevier
Abstract: In this paper we prove that a generalization of complex Π-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 Π-operator across the boundary of the domain is obtained as well as an estimate for the norm of the Π-operator is given. At the end an application of the generalized Π-operator to the solution of Beltrami equations is studied where we give conditions for a solution to realize a local and global homeomorphism.
Peer review: yes
DOI: 10.1016/j.jmaa.2015.09.038
ISSN: 0022-247X
Appears in Collections:CIDMA - Artigos
CHAG - Artigos

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