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Cauchy–Pompeiu representations for higher order elliptic equations in the unit ball

Cauchy–Pompeiu representations for higher order elliptic equations in the unit ball Abstract In this paper we consider the Pompeiu operator in the higher dimensional complex unit ball. The explicit form of its iteration is given. The operator is iterated just once leading to some particular solution to an inhomogeneous bianalytic system. We prove the explicit form of this iteration. Moreover, some further properties, e.g., the kernel space, of the Pompeiu operator are discussed, which gives an application to the pluriharmonic differential system. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Pure and Applied Mathematics de Gruyter

Cauchy–Pompeiu representations for higher order elliptic equations in the unit ball

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Publisher
de Gruyter
Copyright
Copyright © 2011 by the
ISSN
1867-1152
eISSN
1869-6090
DOI
10.1515/apam.2010.041
Publisher site
See Article on Publisher Site

Abstract

Abstract In this paper we consider the Pompeiu operator in the higher dimensional complex unit ball. The explicit form of its iteration is given. The operator is iterated just once leading to some particular solution to an inhomogeneous bianalytic system. We prove the explicit form of this iteration. Moreover, some further properties, e.g., the kernel space, of the Pompeiu operator are discussed, which gives an application to the pluriharmonic differential system.

Journal

Advances in Pure and Applied Mathematicsde Gruyter

Published: May 1, 2011

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