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Sergey Konyagin (Steklov Institute, Moscow)
Thursday 17 February 2011, 15:30-16:30
Basis sets in Banach spaces
- đ¤ Speaker: Sergey Konyagin (Steklov Institute, Moscow)
- đ Date & Time: Thursday 17 February 2011, 15:30 - 16:30
- đ Venue: MR14, CMS
Abstract
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 functions, namely there is a function f whose Fourier series does not converge to f in the uniform metric.
Less known fact is that changing the order of summation will not help either, i.e., for any given rearrangement M of M, there still is a function f whose M-rearranged Fourier series does not converge to f.
But if we still want to stick with the Fourier series as a way of representing continuous functions we may ask whether, for any given f, we may find a (now f-dependent) rearrangement of its Fourier series which converges uniformly to f. The answer to this question is unknown.
In our talk, we address this question in some general setting for bases in Banach spaces.
Series This talk is part of the Applied and Computational Analysis series.
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