Convergence to Zero of Exponential Sums with Positive Integer Coefficients and Approximation by Sums of Shifts of a Single Function on the Line
- 126 Downloads
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 phrasestrigonometric polynomial with positive integer coefficients convergence almost everywhere approximation sum of shifts Lp space
Mathematics Subject Classification42A05 42A32 41A46
Unable to display preview. Download preview PDF.
- S. V. Konyagin, On a question of Pichorides, C. R. Acad. Sci. Paris Ser. I Math., 324 (1997), 385–388.Google Scholar