Real Analysis Exchange

Rearrangements of trigonometric series and trigonometric polynomials.

S. V. Konyagin

Full-text: Open access


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.

Article information

Real Anal. Exchange, Volume 29, Number 1 (2003), 323-334.

First available in Project Euclid: 9 June 2006

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 42A20: Convergence and absolute convergence of Fourier and trigonometric series 42A05: Trigonometric polynomials, inequalities, extremal problems 42A61: Probabilistic methods

trigonometric polynomials trigonometric Fourier series uniform convergence


Konyagin, S. V. Rearrangements of trigonometric series and trigonometric polynomials. Real Anal. Exchange 29 (2003), no. 1, 323--334.

Export citation