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SUMMARY:The Fourier transform of a function of bounded variation: symmetry
  and asymmetry - Elijah Liflyand (Bar-Ilan University)
DTSTART:20190124T150000Z
DTEND:20190124T160000Z
UID:TALK119266@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:New relations between the Fourier transform of a function of b
 ounded variation and the Hilbert transform of its  derivative are revealed
 . The main result is an asymptotic formula for the&nbsp\; cosine Fourier t
 ransform.  Such relations have previously been known only for the sine Fou
 rier transform. To prove the mentioned result\,  not only a different spac
 e is considered but also a new way of proving such theorems is applied.  I
 nterrelations of various function spaces are studied in this context. The 
 obtained results are used for proving  new estimates for the Fourier trans
 form of a radial function and completely new results on the integrability&
 nbsp\; of trigonometric series.  <br><br><br><br><br>
LOCATION:Seminar Room 2\, Newton Institute
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