Rearrangements of Trigonometric Series and Trigonometric Polynomials

2003/03/05 by Sergeĭ Konyagin, S. V. Konyagin, Konyagin, S. V.
Mathematics · #42A05 #42A20 #42A61 #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical Approximation and Integration #advanced mathematical theories #math.CA #math.CO #msc:42A05 #msc:42A20 #msc:42A61

paper · pdf · doi:10.48550/arxiv.math/0303064

arxiv created 2003/03/05 · openalex publication_date 2003/03/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper is related to the following question of P.~L.~Ul'yanov: is it true that for any 2π-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 a problem 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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