Abstract
In this paper we consider the question of a representations of functions from weighed class L 1 [0, 2π] by series with monotonic coefficients concerning trigonometric systems .
Highlights
In this paper we consider the question of a representations of functions from weighed class L1μ[0, 2π] by series with monotonic coefficients concerning trigonometric systems
Riesz [1] proved that there exists a function f0(x) ∈ L1[0, 2π] so that its Fourier series with respect to the trigonometric system does not converge in L1[0, 2π]
There exist functions in the space L1[0, 2π] that cannot be represented by trigonometric series In [5] it is proved in the metric of L1. that there is a weighted space
Summary
Riesz [1] proved that there exists a function f0(x) ∈ L1[0, 2π] so that its Fourier series with respect to the trigonometric system does not converge in L1[0, 2π]. There exist functions in the space L1[0, 2π] that cannot be represented by trigonometric series In [5] it is proved in the metric of L1. In this paper we consider the question of a representations of functions from weighed class L1μ, 0 < μ ≤ 1 by series with monotonic coefficients concerning trigonometric system.
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