Amalgam spaces resp. generalized amalgam spaces (originally called Wiener-type spaces) have been introduced in the early 80's in order to define an analogue of Besov spaces over locally compact Abelian groups. Since there is no dilation over such groups (in contrast to the Euclidean setting) one has to resort the UNIFORM partitions of unity as opposed to dyadic decompositions (related to Paley-Littewood theory for L^p-spaces).

The corresponding spaces have been later called modulation spaces.

Further details are to be given "anytime" later

For the work in Gabor Analysis these Wiener amalgam spaces have turned out to be maximally useful. First of all to choose the ``admissible windows'' (from Wiener's algebra), secondly to describe the (local versus global) behaviour of short-time Fourier transforms, and to understand how the local sampling captures the relevant inforamtion, very much comparable with the situation for band-limited functions or functions of spline-type (discussed elsewhere).

1.1.2009, hgfei