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Théorème de Jordan Friable

In: Analytic Number Theory

Author

Listed:
  • 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)

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.

Suggested Citation

  • Régis de la Bretèche & Gérald Tenenbaum, 2015. "Théorème de Jordan Friable," Springer Books, in: Carl Pomerance & Michael Th. Rassias (ed.), Analytic Number Theory, pages 57-64, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-22240-0_3
    DOI: 10.1007/978-3-319-22240-0_3
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