On a Class of Monogenic Functions with (Logarithmic) Line Singularities

被引：2
|
作者：
Bock, Sebastian [1 ]
机构：
[1] Bauhaus Univ Weimar, Inst Math Phys, Coudraystr 13B, D-99423 Weimar, Germany
来源：
ADVANCES IN APPLIED CLIFFORD ALGEBRAS | 2018年 / 28卷 / 01期
关键词：
Monogenic functions; Line singularities; Recurrence formulae;
D O I：
10.1007/s00006-018-0823-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the article a new class of monogenic functions with (logarithmic) line singularities is studied, which naturally extend the classical system of outer solid spherical monogenics. These functions have special properties with respect to the hypercomplex derivative (generalized Appell property) and can be generated by a three-term recurrence relation. Furthermore, an explicit decomposition of the harmonic Newton kernel is given by means of these functions and a connection to the Cauchy kernel is shown.
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页数：19
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