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Fourier transform of nondecaying functions 
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#1
Feb711, 01:10 AM

P: 625

Hi,
if we consider a constant function [itex]f(x)=1[/itex], it is wellknown 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? 


#2
Feb711, 04:27 PM

Sci Advisor
P: 6,057

I suspect that any bounded function would have an improper (including delta functions) Fourier transform.



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