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 Nov 12 revised Fourier transform of $|x|^{-t}$ edited body May 8 revised Fourier transform of $|x|^{-t}$ edited body Feb 25 comment How much is $\sum_{n\neq 0, n\in Z^d} \frac{\cos(n\cdot x)}{|n|^s}$ @IshanBanerjee: it is the set of $d$ dimensional vector with each component to be integer Feb 22 asked How much is $\sum_{n\neq 0, n\in Z^d} \frac{\cos(n\cdot x)}{|n|^s}$ Feb 12 awarded Supporter Feb 8 comment Fourier transform of $|x|^{-t}$ sorry for the confusion. I've updated it, there should be a "$\sin^{d-2}\theta$" term missing, yes, only when $d=2$, it's gone. I have the same conclusion as you. Feb 8 revised Fourier transform of $|x|^{-t}$ deleted 1 characters in body Feb 8 comment Fourier transform of $|x|^{-t}$ Is this means only for $t\in (d-1,d)$, its Fourier transform is a regular function(with out the point $\xi=1$); for $t\in (0,d-1]$, its Fourier transform is a distribution? Feb 8 revised Fourier transform of $|x|^{-t}$ added 590 characters in body Feb 8 awarded Teacher Feb 6 revised Fourier transform of $|x|^{-t}$ edited body Feb 6 answered Fourier transform of $|x|^{-t}$ Feb 4 revised Fourier transform of $|x|^{-t}$ added 56 characters in body; edited title Feb 4 asked Fourier transform of $|x|^{-t}$ Oct 22 asked Is the dual space of a Banach space Hausdorff? Oct 4 comment density in $L^p$ I do not know what explicitly $f$, $g$ and $h$ are. But I get your idea. I think it works, and the answer is positive. Thank you. Oct 3 awarded Editor Oct 3 comment density in $L^p$ sorry, it should be "defined" Oct 3 revised density in $L^p$ deleted 2 characters in body Oct 1 awarded Student