## Explicit Salem Sets in R^nAdd to your list(s) Download to your calendar using vCal - Rob Fraser (Edinburgh)
- Tuesday 21 January 2020, 14:00-15:00
- WATN-R17 18, Watson Building.
If you have a question about this talk, please contact Hong Duong. In 1981, R. Kaufman showed that the $\tau$-approximable numbers in $\mathbb{R}$ support a measure $\mu$ satisfying $
|\hat{\mu}|\leq C_\epsilon (1+|\xi|) for any $\epsilon>0$. The exponent $-1/(1+\tau)$ is optimal for a set with Hausdorff dimension $2/(1+\tau)$. Sets supporting a measure with nearly optimal pointwise Fourier decay for their Hausdorff dimension are called Salem sets. We show that a higher-dimensional analogue of the $\tau$-approximable numbers is a Salem set. This provides the first explicit example of a Salem set of dimension other than 0, n-1, or n in $\mathbb{R}n$. (Joint work with Kyle Hambrook) This talk is part of the Analysis seminar series. ## This talk is included in these lists:Note that ex-directory lists are not shown. |
## Other listsApplied Mathematics Seminar Series PIPS - Postgraduate Informal Physics Seminars School of Chemistry Seminars## Other talks[Friday seminar]: Irradiated brown dwarfs in the desert The percolating cluster is invisible to image recognition with deep learning Signatures of structural criticality and universality in the cellular anatomy of the brain Provably Convergent Plug-and-Play Quasi-Newton Methods for Imaging Inverse Problems |