- #1
mnb96
- 711
- 5
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?
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?
