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SUMMARY:Quadratic spectral concentration of characteristic functions - Kri
 stina Oganesyan (Universitat Autònoma de Barcelona)
DTSTART:20240716T111500Z
DTEND:20240716T113500Z
UID:TALK218149@talks.cam.ac.uk
DESCRIPTION:A theorem of Donoho and Stark states that decreasing rearrange
 ment increases the quadratic spectral concentration of a square integrable
  function supported on a sufficiently small set. Importantly\, their condi
 tion on the smallness of the support turns out to be necessary. In this ta
 lk\, we restrict ourselves to considering only characeristic functions and
 \, in this setting\, we are able to relax the condition of Donoho and Star
 k. We also discuss various properties of the sets of fixed measure maximiz
 ing the quadratic spectral concentration of their characteristic functions
 . As a corollary\, we obtain a sharp (up to a constant) estimate for the L
 2-norms of non-harmonic trigonometric polynomials with alternating coeffic
 ients 1 and -1.
LOCATION:Seminar Room 1\, Newton Institute
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