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UID:8403@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20140408T110000
DTEND;TZID=Europe/Paris:20140408T120000
DTSTAMP:20241120T210402Z
URL:https://www.i2m.univ-amu.fr/evenements/fourier-dimension-and-modificat
 ions/
SUMMARY:Jörg Schmeling (Lund University\, Sweden): Fourier dimension and m
 odifications
DESCRIPTION:Jörg Schmeling: Fourier dimension was introduced to estimate t
 he Hausdorff dimension of sets in ℝⁿ. However the Fourier transform re
 flects more arithmetic than dimension-like properties and is also hard to 
 compute. In particular it is not clear whether the Fourier dimension is st
 able under unions of sets. In this talk we show that it is not stable unde
 r countable unions. We also introduce several natural modifications that a
 llow to obtain countable stability and yet do not destroy the peculiar pro
 perties that are used in harmonic analysis. In particular new classes of s
 ets\, generalizations of Salem sets\, arise. The talk is based on the work
  of the dynamical systems group in Lund: Magnus Aspenberg\, Fredrik Ekstr
 öm\, Tomas Persson and myself.\nhttps://arxiv.org/abs/1406.1480\n\n&nbsp\
 ;
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Jorg_Schmeling.jpg
CATEGORIES:Séminaire,Ernest
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DTSTART:20140330T030000
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