STARTing Some History Conceptual HA

SOsp(Rd) Test Functions Landscape Classical Appl. Fei/Kaibl Applications Poisson TILS Multipliers Spectral Analysis The Kernel Theorem Operator BGT-Isomorphism bibliography Relevance for Gabor Analysis Just one FT THANKS
The History of Fourier Analysis
From individual function to function spaces
Classical Fourier Series and Fourier transforms;
Questions of pointwise (a.e.) convergence;
Mapping properties, e.g. Hausdorff Young;
Abstract Harmonic Analysis (LCA groups), convolution;
Distribution theory (microlocal analysis);
Computational HA (FFT, FFTW);
Systems Theory, impulse response, transfer function.
GOAL: Moving from the consideration of the individual
function, operator or function spaces to the relationship
between functions on different groups and their connections.
Hans G. Feichtinger
THE Banach Gelfand Triple and its role in Classical Fourier Analysis and Operator Theory