论文标题
almansi-type定理，用于在Clifford代数上的切片定期函数
Almansi-type theorems for slice-regular functions on Clifford algebras
论文作者
论文摘要
我们提出了具有Clifford系数的多项式的Almansi型分解，更一般地用于Clifford代数的切片定期功能。 Emilio Almansi的经典结果于1899年出版，涉及多谐功能，即迭代Laplacian的核心的元素。在这里，我们考虑$ p（x）= \ sum_ {k = 0}^d x^ka_k $的多项式，带有clifford系数$ a_k \ in \ mathbb r_ {n} $，并获得与Zonal Polyharmonics相关的类似分解。我们显示了这种分解与狄拉克（或cauchy-riemann）操作员之间的关系，并将结果扩展到切片规范的函数。
We present an Almansi-type decomposition for polynomials with Clifford coefficients, and more generally for slice-regular functions on Clifford algebras. The classical result by Emilio Almansi, published in 1899, dealt with polyharmonic functions, the elements of the kernel of an iterated Laplacian. Here we consider polynomials of the form $P(x)=\sum_{k=0}^d x^ka_k$, with Clifford coefficients $a_k\in\mathbb R_{n}$, and get an analogous decomposition related to zonal polyharmonics. We show the relation between such decomposition and the Dirac (or Cauchy-Riemann) operator and extend the results to slice-regular functions.
