Series of scalars, vectors, or functions are among the fundamental objects of mathematical
analysis. When the arrangement of the terms is fixed, investigating a series amounts to …

Continuing previous studies of the Beurling zeta function, here, we prove two results,
generalizing long existing knowledge regarding the classical case of the Riemann zeta …

Let X be a Banach space, F be a filter on N. A sequence (en) in X is called an F-basis if for
every x∈ X there is a unique sequence of scalar coefficients (an) such that the partial sums …

The present work is devoted to the problems related to the rearrangements of series in
metrizable topological vector spaces. The idea goes back to Dirichlet (most probably, he …

ON UNIFORMLY CONVERGENT REARRANGEMENTS OF TRIGONOMETRIC FOURIER
SERIES SV Konyagin UDC 517.5 Page 1 Journal of Mathematical Sciences, Vol. 155, No. 1 …

Abstract lcub; xn rcub; with lcub; xn, x* n rcub; biorthogonal is a “uniformly minimal basis with
quasifixed brackets and permutations” of a Banach space X if lcub; xn rcub; and x* n rcub; …

We prove a variant of the transference lemma and by applying it we get a refined version of
the Garsia inequality for orthogonal systems (the case p≥ 2). Moreover we show that the …

The paper is related to the following question of PL Ul'yanov. Is it true that for any 2π-
periodic continuous function f there is a uniformly convergent rearrangement of its …

In [9] we investigated the problem of finding convergent rearrangements to Fourier series of
continuous periodic functions. For motivation and history we refer to that paper, and here …

This article studies the rearrangement problem for Fourier series introduced by PL Ulyanov,
who posed the question if every continuous function on the torus admits a rearrangement of …