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2003-2004 Rearrangements of trigonometric series and trigonometric polynomials.
S. V. Konyagin
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Real Anal. Exchange 29(1): 323-334 (2003-2004).


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.


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S. V. Konyagin. "Rearrangements of trigonometric series and trigonometric polynomials.." Real Anal. Exchange 29 (1) 323 - 334, 2003-2004.


Published: 2003-2004
First available in Project Euclid: 9 June 2006

zbMATH: 1060.42004
MathSciNet: MR2061314

Primary: 42A05 , 42A20 , 42A61

Keywords: trigonometric Fourier series , trigonometric polynomials , Uniform convergence

Rights: Copyright © 2003 Michigan State University Press

Vol.29 • No. 1 • 2003-2004
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