On the existence of universal series by trigonometric system
Sergo A. Episkoposian (Yepiskoposyan)

TL;DR
This paper proves the existence of a universal trigonometric series that can approximate functions in weighted $L^1$ spaces with arbitrary small exceptions, using a specific convergence condition on the coefficients.
Contribution
It introduces a new class of universal trigonometric series with coefficients satisfying a weighted square-summability condition, extending the concept of universality in weighted function spaces.
Findings
Existence of a universal series with specific coefficient conditions
Construction of weighted functions approximating arbitrary functions
Series is universal with respect to rearrangements in weighted $L^1$ spaces
Abstract
In this paper we prove the following: let be a continuous function, increasing in and . Then there exists a series of the form with , , with the following property: for each a weighted function can be constructed, so that the series is universal in the weighted space with respect to rearrangements.
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Taxonomy
TopicsFunctional Equations Stability Results · advanced mathematical theories · Differential Equations and Boundary Problems
