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For distributions the scaling property, $f(ax) = \frac{1}{|a|} \mathcal{F(\frac{u}{a})}$, of the Fourier transform is no longer true. Is there a source that lists which properties of the Fourier transform remain true even for distributions and which are false?

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Are you sure about the failure of the scaling property? – Giuseppe Negro Dec 22 '12 at 1:30
I agree with Guiseppe. The scaling property is commonly exploited with Dirac delta functions. – Ron Gordon Dec 22 '12 at 4:23

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