Hello,(adsbygoogle = window.adsbygoogle || []).push({});

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.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Question on limits and little-o notation

**Physics Forums | Science Articles, Homework Help, Discussion**