论文标题
在全球运算符和fueter映射定理上，用于切片多序分析函数
On the global operator and Fueter mapping theorem for slice polyanalytic functions
论文作者
论文摘要
在本文中，我们证明，在四季度上切片的多芯片分析函数可以被视为某些具有非恒定系数的特殊全球运算符的解决方案，因为它在切片超酚函数的情况下发生。我们还研究了此多序分析设置中Fueter映射定理的扩展版。特别是，我们表明，在轴向对称条件下，始终可以使用我们所谓的聚二线映射来构建燃料常规和聚料机的常规函数。我们还研究了这些结果在Quaternionic单位球上的一些不可或缺的表示。
In this paper, we prove that slice polyanalytic functions on quaternions can be considered as solutions of a power of some special global operator with nonconstant coefficients as it happens in the case of slice hyperholomorphic functions. We investigate also an extension version of the Fueter mapping theorem in this polyanalytic setting. In particular, we show that under axially symmetric conditions it is always possible to construct Fueter regular and poly-Fueter regular functions through slice polyanalytic ones using what we call the poly-Fueter mappings. We study also some integral representations of these results on the quaternionic unit ball.
