# Improper integral

• Mar 30th 2009, 08:40 PM
willki
Improper integral
can there be a Fourier transform of the following integral..??

$sin(1/x)$
• Apr 2nd 2009, 02:21 AM
chisigma
A function $f(*)$ has Fourier Tranform if and only if is $f \in L_{1}$, that means that exists the integral...

$\int_{- \infty}^{+ \infty} |f(x)|\cdot dx$ (1)

But for 'large x' is...

$\sin \frac{1}{x} \approx \frac{1}{x}$

... so that integral (1) doesn't exist... very sorry! (Shake)...

Kind regards

$\chi$ $\sigma$