Timeline for Fourier dimension of the sum of sets
Current License: CC BY-SA 4.0
7 events
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| Sep 8, 2018 at 12:52 | history | edited | Pablo Shmerkin | CC BY-SA 4.0 |
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| Sep 8, 2018 at 12:47 | comment | added | Pablo Shmerkin | @MichaelGaudreau, you're right, it's unclear to me now whether a set of positive Lebesgue measure always has Fourier dimension 1. The fact that the indicator function of the set has no fast decay is not enough to conclude the opposite, though. In this case, however, $C+tC$ has nonempty interior by Newhouse's gap Lemma so the Fourier dimension is $1$. I will edit my answer accordingly. | |
| Sep 3, 2018 at 15:50 | comment | added | MichaelGaudreau | You wrote Marstrand's theorem implies C+tC has positive Lebesgue measure (for almost every $t$), hence C+tC has Fourier dimension 1 (for almost every $t$). I don't think positive Lebesgue measure alone implies full Fourier dimension. See math.stackexchange.com/questions/149660/… | |
| Dec 3, 2010 at 19:22 | vote | accept | Vince | ||
| Nov 29, 2010 at 4:41 | history | edited | Pablo Shmerkin | CC BY-SA 2.5 |
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| Nov 29, 2010 at 4:33 | history | edited | Pablo Shmerkin | CC BY-SA 2.5 |
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| Nov 29, 2010 at 4:22 | history | answered | Pablo Shmerkin | CC BY-SA 2.5 |