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Stetkær, H.

Functional equations on abelian groups with involution. (English) Zbl 0899.39007

Aequationes Math. 54, No. 1-2, 144-172 (1997).
The author investigates generalizations of several functional equations such as d’Alembert’s, Wilson’s, Jensen’s and the functional equation of quadratic functions. The main point is that he replaces terms of the form \(x-y\) by \(x+ \sigma (y)\), where \(\sigma\) is an involution. Moreover a general framework is used which is interesting for itself. The main tool is the notion of a \(K\)-spherical function, where \(K\) is a compact transformation group of a topological group. The paper is very interesting, unifies and generalizes earlier results and shows new perspectives in the considered area.
Reviewer: J.Schwaiger (Graz)

Cited in 6 Reviews
Cited in 49 Documents

MSC:

39B52 Functional equations for functions with more general domains and/or ranges

Keywords:

functional equations on abelian groups; \(K\)-spherical function; d’Alembert functional equation; Wilson functional equation; Jensen functional equation; functional equation of quadratic functions; involution; topological group
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\textit{H. Stetkær}, Aequationes Math. 54, No. 1--2, 144--172 (1997; Zbl 0899.39007)
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