# Fourier transform of non-decaying functions

 P: 625 Hi, if we consider a constant function $f(x)=1$, it is well-known that its Fourier transform is the delta function, in other words: $$\int_{-\infty}^{+\infty}e^{-i\omega x}dx = \delta(\omega)$$ The constant function does not tend to zero at infinity, so I was wondering: are there other functions that do not tend to zero at infinity but do have a Fourier transform? I can think only of linear combinations of $$e^{-i\omega x}$$. Are there others?