## Real Analysis Exchange

### Rearrangements of trigonometric series and trigonometric polynomials.

S. V. Konyagin

#### Abstract

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

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

Dates
First available in Project Euclid: 9 June 2006