# Math Help - Improper integral

1. ## Improper integral

can there be a Fourier transform of the following integral..??

$sin(1/x)$

2. 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! ...

Kind regards

$\chi$ $\sigma$