Summary
If a groupG permutes a setI, andM is a multiplicative abelian group, a representation ofG onM I is given by permutation of coordinates. TheG-module homomorphisms intoM I arise from exponential maps. This framework encompasses those systems of functional equations that characterize generalized hyperbolic functions.
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References
Artin, M.,Algebra. Prentice-Hall, New Jersey, 1991.
Baker, J. A., Lawrence, J. andZorzitto, F.,The stability of the equation f(x + y) = f(x)f(y). Proc. Amer. Math. Soc.74 (1979), 242–246.
Förg-Rob, W. andSchwaiger, J.,On the stability of a system of functional equations characterizing generalized hyperbolic and trigonometric functions. Aequationes Math.45 (1993), 285–297.
Schwaiger, J.,On the generalized hyperbolic functions and their characterization by functional equations. Aequationes Math.43 (1992), 198–216.
Székelihidi, L.,Convolution type functional equations on topogical abelian groups. World Scientific Publishing, Singapore, 1991.