The material covering the WINTER TERM 06 / 07 at the end ! ! ! A NEW APPROACH TO HARMONIC ANALYSIS : NUHAG , COURSE MATERIAL 2006 / 2007

The results are non-trivial for the real line R, but are formulated for the d−dimensional Euclidean space R, viewed as a prototype for a locally compact Abelian group (with the usual addition of vectors and the topology provided by the Euclidian metric). 1 We start with the description of Mb(G), the space of bounded linear measures, as the dual space of C0, which is naturally endowed with a convolution structure.