This is an announcement for the paper "On the existence of universal series by trigonometric system" by Sergo A. Episkoposian.

Abstract: In this paper we prove the following: let $\omega(t)$ be a continuous function, increasing in $[0,\infty)$ and $\omega(+0)=0$. Then there exists a series of the form $$\sum_{k=-\infty}^\infty C_ke^{ikx} \ \ with \ \ \sum_{k=-\infty}^\infty C^2_k \omega(|C_k|)<\infty ,\ \ C_{-k}=\overline{C}_k, \eqno$$ with the following property: for each $\varepsilon>0$ a weighted function $\mu(x), 0<\mu(x) \le1, \left | { x\in[0,2\pi]: \mu(x)\not =1 } \right | <\varepsilon $ can be constructed, so that the series is universal in the weighted space $L_\mu^1[0,2\pi]$ with respect to rearrangements.

Archive classification: math.FA

Mathematics Subject Classification: 42A20

Submitted from: sergoep@ysu.am

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1109.3805

or

http://arXiv.org/abs/1109.3805