Fourier dimension and modifications

Jörg Schmeling
Lund University, Sweden

Date(s) : 08/04/2014   iCal
11 h 00 min - 12 h 00 min

Fourier dimension was introduced to estimate the Hausdorff dimension of sets in ℝⁿ. However the Fourier transform reflects more arithmetic than dimension-like properties and is also hard to compute. In particular it is not clear whether the Fourier dimension is stable under unions of sets. In this talk we show that it is not stable under countable unions. We also introduce several natural modifications that allow to obtain countable stability and yet do not destroy the peculiar properties that are used in harmonic analysis. In particular new classes of sets, generalizations of Salem sets, arise. The talk is based on the work of the dynamical systems group in Lund: Magnus Aspenberg, Fredrik Ekström, Tomas Persson and myself.



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