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

$\displaystyle sin(1/x)$

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- Mar 30th 2009, 08:40 PMwillkiImproper integral
can there be a Fourier transform of the following integral..??

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

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

But for 'large x' is...

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

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

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$