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.
Colzani, L., Gigante, G., Vegas, A. (2014). Localization for Riesz means of Fourier expansions. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 366(12), 6229-6245 [10.1090/S0002-9947-2014-06076-5].
Localization for Riesz means of Fourier expansions
COLZANI, LEONARDO;
2014
Abstract
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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