Timeline for What can be said about the Fourier transforms of characteristic functions?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Apr 24, 2014 at 11:06 | comment | added | Piero D'Ancona | I think it's hopeless to look for a characterization in terms of norms or asymptotic properties; these would not distinguish small perturbations of a characteristic function. Maybe you could use the fact that they coincide with their square, so that the transform $f$ satisfies $f*f=f$ | |
| Apr 24, 2014 at 1:07 | answer | added | guest007 | timeline score: 1 | |
| Apr 23, 2014 at 18:30 | answer | added | Joni Teräväinen | timeline score: 7 | |
| Apr 22, 2014 at 23:30 | history | edited | Joni Teräväinen | CC BY-SA 3.0 |
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| Apr 22, 2014 at 23:22 | comment | added | Joni Teräväinen | By regularity of the Fourier transform, I meant both its decay and smoothness. If these Fourier transforms are always entire, then I just mean decay, but if we for example take a Cantor-type set extending to infinity with positive finite measure, I don't see directly why the Fourier transform should be analytic. | |
| Apr 22, 2014 at 23:05 | comment | added | Christian Remling | I don't think we expect the regularity of $A$ to affect the REGULARITY of $\widehat{\chi_A}$ (rather, regularity/smoothness <-> decay is the received wisdom). | |
| Apr 22, 2014 at 18:52 | history | asked | Joni Teräväinen | CC BY-SA 3.0 |