Locally compact abelian groups and the foundations of harmonic analysis

Abstract

Abstract The most fundamental locally compact abelian groups are the following: R. the additive group of real numbers; Z, the additive group of integers; and 11’, the multiplicative group of complex numbers of absolute value I. The group 1I’ is isomorphic, as a topological group, to R/Z; this is the significance of the mapping x 1-1e2(see also the discussion on the algebra F1(‘JI’) in Section 1.1).