Zum Begriff der Analytizität auf zusammenhängenden Iokalkompakten Gruppen

Abstract

Several definitions of analyticity of functions on locally compact groups are introduced and tested in connection with the proprties of the Fourier coefficients on a compact solenoid. It is proved that absolute convergence of the Fourier series does not follow from analyticity and that a rapidly decreasing sequence of Fourier coefficients of a function, which is analytic on a dense subset, need not exponentially rapidly decrease. On the other hand, on compact groups functions with exponentially rapidly decreasing Fourier coefficients are analytic.