有限维交换结合代数中单演函数的构造性描述
Constructive description of monogenic functions in a finite-dimensional commutative associative algebra
摘要：
设$\mathbb{A}_n^m$是复数域上具有$m$幂等元的任意$n$ -维交换结合代数.设$e_1=1,e_2,e_3$是$\mathbb{A}_n^m$中在实数域上线性无关的元素。我们考虑变量$xe_1+ye_2+ze_3$的单演（即在Gateaux意义下连续和可微）函数，其中$x,y,z$是实数，并通过复变的全纯函数得到所有提到的函数的构造性描述.从这一描述可以得出，单演函数具有所有阶的加托导数。
英文摘要：
Let $\mathbb{A}_n^m$ be an arbitrary $n$-dimensional commutative associative algebra over the field of complex numbers with $m$ idempotents. Let $e_1=1,e_2,e_3$ be elements of $\mathbb{A}_n^m$ which are linearly independent over the field of real numbers. We consider monogenic (i.e. continuous and differentiable in the sense of Gateaux) functions of the variable $xe_1+ye_2+ze_3$ where $x,y,z$ are real, and obtain a constructive description of all mentioned functions by means of holomorphic functions of complex variables. It follows from this description that monogenic functions have Gateaux derivatives of all orders.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
