# Analytic representation of functions and a new quasi-analyticity threshold

### Abstract

We characterize precisely the possible rate of decay of the anti-analytic half of a trigonometric series converging to zero almost everywhere.

## Authors

Gady Kozma

Faculty of Mathematics and Computer Science, Weizmann Institute of Science, 76100 Rehovot, Israel

Alexander Olevskiĭ

School of Mathematical Sciences, Tel Aviv University, 69978 Tel Aviv, Israel