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I was studying the theorem of smoothness/compactness in Fourier theory and at the very last step of the proof one gets the result that [itex]\omega F(\omega)\to 0[/itex] when [itex]x\to \infty[/itex]. The author of the book writes this result in little-o notation as: [tex]\omega F(\omega) = o(|\omega|^{-1})[/tex] which I understand, but then he deduces directly that: [tex]F(\omega)=o(|\omega|^{-2})[/tex]. Can anyone explain this last step? Thanks.

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# Question on limits and little-o notation

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