Rearrangements of Trigonometric Series and Trigonometric Polynomials
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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