Real Analysis Exchange

Rearrangements of trigonometric series and trigonometric polynomials.

S. V. Konyagin

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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

Permanent link to this document
https://projecteuclid.org/euclid.rae/1149860196

Mathematical Reviews number (MathSciNet)
MR2061314

Zentralblatt MATH identifier
1060.42004

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

Keywords
trigonometric polynomials trigonometric Fourier series uniform convergence

Citation

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


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