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The teodorescu operator in Clifford Analysis

Chinese Annals of Mathematics,Series B 2012年第4期33卷 625-640页

作者： F.BRACKX H.De SCHEPPER M.E. LUNA-ELIZARRARS M.SHAPIRO Clifford Research Group Faculty of Engineering and Architecture Ghent University Belgium Instituto Politcnico Nacional Mexico City Mexico

Euclidean Clifford analysis is a higher dimensional function theory centred around monogenic functions, i.e., null solutions to a first order vector valued rotation in- variant differential operator called the Dirac operator. More recently, Hermitian Clifford analysis has emerged as a new branch, offering yet a refinement of the Euclidean case; it focuses on the simultaneous null solutions, called Hermitian monogenic functions, to two Hermitian Dirac operators and which are invariant under the action of the unitary group. In Euclidean Clifford analysis, the teodorescu operator is the right inverse of the Dirac operator __0. In this paper, teodorescu operators for the Hermitian Dirac operators c9~_ and 0_~, are constructed. Moreover, the structure of the Euclidean and Hermitian Teodor- escu operators is revealed by analyzing the more subtle behaviour of their components. Finally, the obtained inversion relations are still refined for the differential operators is- suing from the Euclidean and Hermitian Dirac operators by splitting the Clifford algebra product into its dot and wedge parts. Their relationship with several complex variables theory is discussed.

关键词： Clifford analysis teodorescu operator Dirac operator

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Higher Order teodorescu operators in Superspace

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Journal of Mathematical Research with Applications 2015年第6期35卷 643-652页

作者： Hongfen YUAN Yuying QIAO College of Science Hebei University of Engineering College of Mathematics and Information Science Hebei Normal University

We investigate some fundamental properties of the higher order teodorescu operators which are defined by the high order Cauchy-Pompeiu formulas in superspace. Moreover,we get an expansion of Almansi type for k-supermonogenic functions in sense of the teodorescu operators. By the expansion, a Morera type theorem, a Painleve theorem and a uniqueness theorem for k-supermonogenic functions are obtained.

关键词： superspace teodorescu operator k-supermonogenic functions Morera type theorem Painleve theorem uniqueness theorem

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