BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Basis sets in Banach spaces - Sergey Konyagin (Steklov Institute\,
  Moscow)
DTSTART:20110217T153000Z
DTEND:20110217T163000Z
UID:TALK29350@talks.cam.ac.uk
CONTACT:6743
DESCRIPTION:As it is well-known\, trigonometric system M = (e^{ikx})\, in 
 its standard ordering\, does not form a basis for the space of periodic co
 ntinuous functions\, namely there is a function f whose Fourier series doe
 s not converge to f in the uniform metric.\n\nLess known fact is that chan
 ging the order of summation will not help either\, i.e.\, for any given re
 arrangement M* of M\, there still is a function f* whose M*-rearranged Fou
 rier series does not converge to f*.\n\nBut if we still want to stick with
  the Fourier series as a way of\nrepresenting continuous functions we may 
 ask whether\, for any given f\, we may find a (now f-dependent) rearrangem
 ent of its Fourier series which converges uniformly to f. The answer to th
 is question is unknown.\n\nIn our talk\, we address this question in some 
 general setting for bases in Banach spaces.
LOCATION:MR14\, CMS
END:VEVENT
END:VCALENDAR