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Suppose F has discrete Fourier transform where unless for some , in which case (or 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: 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 &gt; works...

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# Regularity of sparse Fourier transforms

Suppose F has discrete Fourier transform where unless for some , in which case (or 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 &gt; works...