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Basis sets in Banach spaces

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  • UserSergey Konyagin (Steklov Institute, Moscow)
  • ClockThursday 17 February 2011, 15:30-16:30
  • HouseMR14, CMS.

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(Note that this talk has been delayed by 30 mins to allow attendance at Terence Tao's talk at INI)

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.

This talk is part of the Applied and Computational Analysis series.

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