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Title: Spherical Pi-type operators in Clifford analysis and applications
Author: Cheng, Wanqing
Ryan, John
Kähler, Uwe
Keywords: Singular integral operator
Beltrami equation
Issue Date: Jun-2017
Publisher: Springer Verlag
Abstract: The Pi-operator (Ahlfors–Beurling transform) plays an important role in solving the Beltrami equation. In this paper we define two Pi-operators on the n-sphere. The first spherical Pi-operator is shown to be an L_2 isometry up to isomorphism. To improve this, with the help of the spectrum of the spherical Dirac operator, the second spherical Pi-operator is constructed as an isometric L_2-operator over the sphere. Some analogous properties for both Pi-operators are also developed. We also study the applications of both spherical Pi-operators to the solution of the spherical Beltrami equations.
Peer review: yes
DOI: 10.1007/s11785-017-0641-0
ISSN: 1661-8254
Appears in Collections:CIDMA - Artigos
CHAG - Artigos

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