- #1

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## Main Question or Discussion Point

Hi,

if we consider a constant function [itex]f(x)=1[/itex], it is well-known that its Fourier transform is the

[tex]\int_{-\infty}^{+\infty}e^{-i\omega x}dx = \delta(\omega)[/tex]

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 [tex]e^{-i\omega x}[/tex]. Are there others?

if we consider a constant function [itex]f(x)=1[/itex], it is well-known that its Fourier transform is the

*delta function*, in other words:[tex]\int_{-\infty}^{+\infty}e^{-i\omega x}dx = \delta(\omega)[/tex]

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 [tex]e^{-i\omega x}[/tex]. Are there others?