Can anyone provide or give an expression in the sense of distribution theory for the functions $|x|^{s} , \log|x| $? I mean I would like to evaluate the Fourier transform $ \int_{-\infty}^{\infty}f(x)\exp(-iux) $ of these transforms in case it is possible.
Fourier transform of $\log x$ $ |x|^{s} $ and $\log|x| $
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fourier-analysis
integral-transforms
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0Do you want the Fourier transform of $|x|^s$ or $|x|^s\log x$? (the first is in the body, the second in the title) – 2012-04-28
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0i am looking for the fourier transform of all $ |x|^{s} 4 and $log|x| $ although by differntiation with respect to 'x' i supsect they are all related. – 2012-04-28