mnb96
- 711
- 5
Hi,
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?
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?