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Hard Summation, Olevskii, Tao and Walsh
Author(s) -
Körner T. W.
Publication year - 2006
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s002460930601890x
Subject(s) - mathematics , fourier series , mathematical proof , context (archaeology) , series (stratigraphy) , fourier transform , calculus (dental) , fourier sine and cosine series , algebra over a field , wavelet , fourier analysis , pure mathematics , mathematical analysis , computer science , geometry , artificial intelligence , fractional fourier transform , medicine , paleontology , dentistry , biology
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. 2000 Mathematics Subject Classification 42A20 (primary), 42C10, 42C20 (secondary).