| Higher Order Teodorescu Operators in Superspace |
| Received:October 19, 2014 Revised:September 14, 2015 |
| Key Words:
superspace Teodorescu operator $k$-supermonogenic functions Morera type theorem Painleve theorem uniqueness theorem
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| Fund Project: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). |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2015.06.006 |
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