The aim is the point out the important role which is played by uniform partitions of unity for the development of fundamental concepts for a functional analytic treatment of key questions of Harmonic Analysis over locally compact Abelian groups (including the classical case G =R^d). It is the also the basis for a new way of introducing convolution and the Fourier Stieltjes transform, but also essential for the definition of Wiener amalgam spaces.

*based on the slides of the FFT talk 2021