17568

A Property of the Haar Measure of Some Special LCA Groups.

245

248

4

The Euclidean group (Rn,+) where (n(element of)N), plays a key role in harmonic analysis. If we consider the Lebesgue measure d(mu)Rn(x) as the Haar measure of this group then 1/2d(mu) Rn(2x)=d(mu)Rn(x). In this article we look for LCA groups K, whose Haar measures have a similar property. In fact we will show that for some LCA groups K with the Haar measure (mu)K, there exists a constant CK>0 such that (mu)K(A)= CK(mu)K (A^2) for every measurable subset A of K. Moreover we will characterize this constant for some special groups.

1201490