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The representation of functions (or objects which are in some generalize the notion of function) as constant linear combinations of sines and cosines at integer multiples of a given frequency, as Fourier transforms or as Fourier integrals.

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Existence of the inverse Fourier transform, Carr Madan

I have a function $C_T(k)$ that is not $L_1$, because its limit in negative infinity is a constant. So I dampened it by $ e^{\alpha k} $. Let's call the transformed function (of the dampened function) …
Marine Galantin's user avatar