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CATEGORIES:Applied and Computational Analysis
SUMMARY:Basis sets in Banach spaces - Sergey Konyagin (Ste
klov Institute\, Moscow)
DTSTART;TZID=Europe/London:20110217T153000
DTEND;TZID=Europe/London:20110217T163000
UID:TALK29350AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/29350
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 continuous funct
ions\, namely there is a function f whose Fourier
series does not converge to f in the uniform metri
c.\n\nLess known fact is that changing the order o
f summation will not help either\, i.e.\, for any
given rearrangement M* of M\, there still is a fun
ction f* whose M*-rearranged Fourier series does n
ot converge to f*.\n\nBut if we still want to stic
k with the Fourier series as a way of\nrepresentin
g continuous functions we may ask whether\, for an
y given f\, we may find a (now f-dependent) rearra
ngement of its Fourier series which converges unif
ormly to f. The answer to this question is unknown
.\n\nIn our talk\, we address this question in som
e general setting for bases in Banach spaces.
LOCATION:MR14\, CMS
CONTACT:
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