Real Analysis Exchange
- Real Anal. Exchange
- Volume 29, Number 1 (2003), 323-334.
Rearrangements of trigonometric series and trigonometric polynomials.
The paper is related to the following question of P.L.Ul'yanov. Is it true that for any $2\pi$-periodic continuous function $f$ there is a uniformly convergent rearrangement of its trigonometric Fourier series? In particular, we give an affirmative answer if the absolute values of Fourier coefficients of $f$ decrease. Also, we study how to choose $m$ terms of a trigonometric polynomial of degree $n$ to make the uniform norm of their sum as small as possible.
Real Anal. Exchange, Volume 29, Number 1 (2003), 323-334.
First available in Project Euclid: 9 June 2006
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Konyagin, S. V. Rearrangements of trigonometric series and trigonometric polynomials. Real Anal. Exchange 29 (2003), no. 1, 323--334. https://projecteuclid.org/euclid.rae/1149860196