Localization for Riesz means of Fourier expansions

Colzani, Leonardo; Gigante, Giacomo; Vargas, Ana

doi:10.1090/S0002-9947-2014-06076-5

Localization for Riesz means of Fourier expansions
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by Leonardo Colzani, Giacomo Gigante and Ana Vargas PDF

Trans. Amer. Math. Soc. 366 (2014), 6229-6245 Request permission

Abstract:

The classical Riemann localization principle states that if an integrable function of one variable vanishes in an open set, then its Fourier expansion converges to zero in this set. This principle does not immediately extend to several dimensions, and here we study the Hausdorff dimension of the sets of points where localization for Riesz means of Fourier expansions may fail.

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