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show/hide this revision's text 2 Made a bit cleaer.

Suppose F has discrete Fourier transform (a\sb n) where a\sb n=0 unless n=2^k for some k>0 , in which case a\sb n=1/k (or a\sb n=1/k^2 if you want: I'm happy with anything polynomial). What sort of regularity conditions does F have? Is it Holder continuous, or not?

To be explicit: [F(x)=\sum\sb {k=1}^\infty k^{-2} \exp(ix2^k)] for example.

More generally, I'm interested in two dimensional (discrete) Fourier transforms: is there a good reference for this sort of thing?

Edit: Slight bug in the sidebar LaTeX converter: it didn't like k>0 as the > gets interpretted as a tag. Manually changing it to > works...
show/hide this revision's text 1

Regularity of sparse Fourier transforms

Suppose F has discrete Fourier transform (a\sb n) where a\sb n=0 unless n=2^k for some k>0 , in which case a\sb n=1/k (or a\sb n=1/k^2 if you want: I'm happy with anything polynomial). What sort of regularity conditions does F have? Is it Holder continuous, or not?

More generally, I'm interested in two dimensional (discrete) Fourier transforms: is there a good reference for this sort of thing?

Edit: Slight bug in the sidebar LaTeX converter: it didn't like k>0 as the > gets interpretted as a tag. Manually changing it to > works...