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42a20 (primary)

Bulletin of the London Mathematical Society (1)

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HARD SUMMATION, OLEVSKII, TAO AND WALSH
T. W. KÖRNER
Journal:

Bulletin of the London Mathematical Society / Volume 38 / Issue 5 / October 2006

Published online by Cambridge University Press:

20 September 2006, pp. 705-729

Print publication:

October 2006
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Tao has shown that hard summation (summing Fourier-type series by using terms in order of decreasing size of the Fourier coefficients) works for wavelets, but the present author has shown that it fails for classical Fourier series. This paper, which is intended for a general audience, exhibits the underlying ideas in the context of Haar and Walsh series, where many of the proofs simplify.