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H. Stetkær 《Aequationes Mathematicae》1997,54(1-2):144-172
Summary We produce complete solution formulas of selected functional equations of the formf(x +y) ±f(x + σ (ν)) = Σ
I
2
=1
g
l
(x)h
l
(y),x, y∈G, where the functionsf,g
1,h
1 to be determined are complex valued functions on an abelian groupG and where σ:G→G is an involution ofG. The special case of σ=−I encompasses classical functional equations like d’Alembert’s, Wilson’s first generalization of it, Jensen’s equation and
the quadratic equation. We solve these equations, the equation for symmetric second differences in product form and similar
functional equations for a general involution σ. 相似文献
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Henrik Stetkær 《Semigroup Forum》2001,63(3):466-468
No abstract.
November 15, 1999 相似文献
4.
Henrik Stetkær 《Aequationes Mathematicae》2016,90(2):407-409
If \({f, g : G \to \mathbb{C}}\), f ≠ 0, is a solution of Wilson’s functional equation on a group G, then g is a d’Alembert function. 相似文献
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Aequationes mathematicae - Let G be a group, and let $$\chi $$ and $$\mu $$ be characters of G. We find the solutions of the functional equation $$f(xy) = f(x)\chi (y) + \mu (x)f(y)$$ , $$x,y \in... 相似文献
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Henrik Stetkær 《Aequationes Mathematicae》2016,90(6):1147-1168
We find the solutions of the cosine addition law with an additional term, including the case of the cosine addition law on semigroups. They are expressed in terms of multiplicative functions and solutions of the sine addition law, apart from an obvious exception. On groups multiplicative and additive functions suffice. As an application we solve extensions of Butler’s problem on semigroups. 相似文献