Lebesgue points and convergence over cone-like sets

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Abstract

We generalize the well known Lebesgue's theorem about the convergence of Fejér means for higher dimensions. Under some conditions on θ, we show that the summability means σT θ f of a function f from the largest Wiener amalgam space W(L1, ℓ∞)(ℝd) converge to f at each modified Lebesgue point, whenever T → ∞ and T is in a cone-like set. The result holds for the Weierstrass, Abel, Picar, Bessel, Fejér, Cesàro, de La Vallée-Poussin, Rogosinski and Riesz summations.

Original languageEnglish
Pages (from-to)65-83
Number of pages19
JournalJaen Journal on Approximation
Volume9
Issue number1
Publication statusPublished - Jan 1 2017

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Keywords

  • Cone-like sets
  • Fejér summability
  • Fourier series
  • Fourier transforms
  • Lebesgue points
  • θ-summability

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis

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