Higher Order Teodorescu Operators in Superspace
Received:October 19, 2014  Revised:September 14, 2015
Key Word: superspace   Teodorescu operator   $k$-supermonogenic functions   Morera type theorem   Painleve theorem   uniqueness theorem  
Fund ProjectL:Supported by the TianYuan Special Funds of the National Natural Science Foundation of China (Grant No.11426082), the National Natural Science Foundation of China (Grant No.10771049) and the Science Foundation of Hebei Province (Grant No.A2015402034).
Author NameAffiliation
Hongfen YUAN College of Science, Hebei University of Engineering, Hebei 056038, P. R. China 
Yuying QIAO College of Mathematics and Information Science, Hebei Normal University, Hebei 050024, P. R. China 
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      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.
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