Analysis Mathematica

, Volume 44, Issue 2, pp 163–183 | Cite as

Convergence to Zero of Exponential Sums with Positive Integer Coefficients and Approximation by Sums of Shifts of a Single Function on the Line



We prove that there is a sequence of trigonometric polynomials with positive integer coefficients, which converges to zero almost everywhere. We also prove that there is a function f: ℝ → ℝ such that the sums of its shifts are dense in all real spaces L p (ℝ) for 2 ≤ p < ∞ and also in the real space C0(R).

Key words and phrases

trigonometric polynomial with positive integer coefficients convergence almost everywhere approximation sum of shifts Lp space 

Mathematics Subject Classification

42A05 42A32 41A46 


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.Laboratory “Multivariate approximation and applications”, Department of Mechanics and MathematicsMoscow State UniversityMoscowRussia
  2. 2.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia

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