The Banach Gelfand Triple based on the Segal Algebra S_o(R^d)
will be described, which is a suitable Banach algebra of test function, invariant under the Fourier transform. It is a dense
subspace of L^2(R^d), and can often take the role of the Schwartz
space of rapidely descreasing functions. Its dual consists of
all tempered distributions which have a bounded STFT (Short time
Fourier Transform).

The space (together with the intermediate Hilbert space) are
universally useful for many questions related to Fourier analysis
or time-frequency analysis.