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 Spherical Pi-type operators in Clifford analysis and applications
Please use this identifier to cite or link to this item http://hdl.handle.net/10773/17745

title: Spherical Pi-type operators in Clifford analysis and applications
authors: Cheng, Wanqing
Ryan, John
Kähler, Uwe
keywords: Singular integral operator
Pi-Operator
Spectrum
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.
URI: http://hdl.handle.net/10773/17745
ISSN: 1661-8254
publisher version/DOI: http://dx.doi.org/10.1007/s11785-017-0641-0
source: Complex Analysis and Operator Theory
appears in collectionsCIDMA - Artigos

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