The so-called Banach Gelfand Triple $(S_0,L^2,S'_0)$ allows to provide a framework for operators relevant for Fourier analysis and the corresponding function spaces which allow for the best possible description of these operators. In particular, one can questions about Fourier multipliers or convolution operators in a very natural way. In addition the so-called kernel theorem allows to characterize operators from S_O to S'_0 through distributional kernels in S'_0(of two variables), which in turn can be used to discuss questions of discrete approximation (via FFT and matrix multiplication). Details will be given later.

THIS TALK HAS NOT been given in this form! HGFei 31.07.2019