超空间上高阶Teodorescu算子

Higher Order Teodorescu Operators in Superspace

中文关键词:  超空间  Teodorescu算子  $k$-超正则函数  Morera型定理  开拓定理  唯一性定理

英文关键词:superspace  Teodorescu operator  $k$-supermonogenic functions  Morera type theorem  Painleve theorem  uniqueness theorem

中文摘要:

      本文首先由超空间上Cauchy-Pompeiu公式定义了超空间上高阶Teodorescu算子,研究了此类算子的一些基本性质.其次,利用此类算子,我们得到了$k$-超正则函数的Almansi型展开. 最后运用这个展开,我们证明了$k$-超正则函数的Morera型定理、开拓定理和唯一性定理.

英文摘要:

      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.