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?
Properties of Fourier transform of distributions
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fourier-analysis
distribution-theory
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3Are you sure about the failure of the scaling property? – 2012-12-22
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0I agree with Guiseppe. The scaling property is commonly exploited with Dirac delta functions. – 2012-12-22