Abstract
I consider representations of functions on the circle by power series (= trigonometric series with positive frequencies) which converge almost everywhere. If it exists, such a representation is always unique. However, in contrast to Riemannian theory, it may differ from the classical Fourier expansion, even for a smooth function [1]. I'll give a survey of the subject and discuss the most recent progress [2].
| Original language | English |
|---|---|
| Pages (from-to) | 9-10 |
| Number of pages | 2 |
| Journal | Real Analysis Exchange |
| Volume | 33 |
| Issue number | 1 |
| State | Published - 2008 |