University of Birmingham > Talks@bham > Analysis seminar > Large sets without Fourier restriction theorems

Large sets without Fourier restriction theorems

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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 Lp(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.

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