Large sets without Fourier restriction theorems

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• Constantin Bilz (Birmingham)
• Tuesday 14 January 2020, 14:00-15:00
• WATN-R17 18, Watson Building.

If you have a question about this talk, please contact Hong Duong.

It was recently established that Fourier restriction theorems have implications for the structure of Lebesgue sets of Fourier transforms. On the other hand, no methodical study of these sets is available. In this talk, we construct a function that lies in L^p(Rd) for every p>1 and whose Fourier transform has no Lebesgue points in a Cantor set of full Hausdorff dimension. We combine this with recent results in restriction theory to prove a lack of valid relations between the Hausdorff dimension of a set and the range of restriction exponents for measures supported in the set.

This talk is part of the Analysis seminar series.

This talk is included in these lists:

• Analysis seminar
• School of Mathematics events
• WATN-R17 18, Watson Building

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