Théorème de Jordan Friable

Régis de la Bretèche () and Gérald Tenenbaum ()
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Régis de la Bretèche: Université Paris Diderot-Paris 7, Institut de Mathématiques de Jussieu-Paris Rive Gauche, UMR 7586
Gérald Tenenbaum: Université de Lorraine, Institut Élie Cartan

A chapter in Analytic Number Theory, 2015, pp 57-64 from Springer

Abstract: Abstract Extending a previous result, we show that, for the friable summation method, the Fourier series of any normalized function F with bounded variation on the unidimensional torus converges pointwise to F while avoiding the Gibbs phenomenon. We also prove that the convergence is uniform when F is continuous and provide an effective bound for the rate when F satisfies a uniform Lipschitz condition.

Keywords: Friable integers; Friable summation; Summation methods; Fourier series; Gibbs phenomenon; Functions of bounded variation; Jordan’s theorem; Integers free of large prime factors; Primary: 11N25; 42A24; secondary: 42A20 (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-22240-0_3

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DOI: 10.1007/978-3-319-22240-0_3

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