Analysis Mathematica

, Volume 44, Issue 2, pp 163–183

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

• P. A. Borodin
• S. V. Konyagin
Article

## Abstract

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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