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 . I'll give a survey of the subject and discuss the most recent progress .
|Number of pages||2|
|Journal||Real Analysis Exchange|
|State||Published - 2008|