We prove that spectral synthesis holds on a discrete Abelian group G if and only if the torsion free rank of G is finite.

In this note the stability theorem of Albert and Baker concerning the n-th difference equation is proved by using invariant means.

The result of J. Baker, J. Lawrence and F. Zorzitto on the stability of the equation $f(x + y) = f(x)f(y)$ is generalized by proving the following theorem: if $...