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-supermo...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.展开更多
基金Supported by the Tian Yuan Special Funds of the National Natural Science Foundation of China(Grant No.11426082)the National Natural Science Foundation of China(Grant No.10771049)the Science Foundation of Hebei Province(Grant No.A2015402034)
文摘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.
