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 Hausdor dimension of the sets of points where localization for Riesz means of Fourier expansions may fail.
Localization for Riesz means of Fourier expansions
GIGANTE, Giacomo;
2013-01-01
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 Hausdor dimension of the sets of points where localization for Riesz means of Fourier expansions may fail.File allegato/i alla scheda:
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