Abstract
Every measurable function f on the circle can be represented as a sum of harmonics with positive spectrum, (formula presented) converging in measure. For convergence almost everywhere this is not true. We discuss several other sets Λ ⊂ ℤ for which one might get a Menshov type representation converging almost everywhere or in measure.
| Translated title of the contribution | An "analytic" version of Menshov's representation theorem |
|---|---|
| Original language | English |
| Pages (from-to) | 219-222 |
| Number of pages | 4 |
| Journal | Comptes Rendus de l'Academie des Sciences - Series I: Mathematics |
| Volume | 331 |
| Issue number | 3 |
| DOIs | |
| State | Published - 1 Aug 2000 |