D'Alembert's functional equations on metabelian groups

被引：0
|
作者：
Stetkær H. [1 ]
机构：
[1] Department of Mathematics, University of Aarhus, Ny Munkegade
来源：
aequationes mathematicae | 2000年 / 59卷 / 3期
关键词：
Functional equation of d'alembert; Metabelian;
D O I：
10.1007/s000100050130
中图分类号：
学科分类号：
摘要：
We extend d'Alembert's classical functional equation by replacing the domain of definition R of the solutions by a metabelian group G and simultaneously replacing the group involution by an arbitrary involution of G. We find all complex valued solutions. In particular we show that the continuous solutions have the same form as in the abelian case if G is connected. © Birkhäuser Verlag, 2000.
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页码：306 / 320
页数：14
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