On a generalized Appell system and monogenic power series
On a generalized Appell system and monogenic power series
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关于广义 Appell 系统和单基因幂级数
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
K. Gürlebeck
中科院分区：
文献类型：
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作者：
S. Bock;K. Gürlebeck
最近，几位作者构建了 ℝ3 中的单基因多项式的 Appell 系统。本文的主要目的是描述另一个在平方可积四元数值函数空间中完备的 Appell 系统。提出了一种基于Appell多项式的新泰勒型级数展开式，它可以与复杂一维情况类似地与相应的傅立叶级数相关。这些结果可用于描述超复导数、单基因函数的单基因原语以及单基因狄利克雷空间的函数表征。 Copyright © 2009 John Wiley & Sons, Ltd.
Recently Appell systems of monogenic polynomials in ℝ3 were constructed by several authors. Main purpose of this paper is the description of another Appell system that is complete in the space of square integrable quaternion‐valued functions. A new Taylor‐type series expansion based on the Appell polynomials is presented, which can be related to the corresponding Fourier series analogously as in the complex one‐dimensional case. These results find applications in the description of the hypercomplex derivative, the monogenic primitive of a monogenic function and the characterization of functions from the monogenic Dirichlet space. Copyright © 2009 John Wiley & Sons, Ltd.