Restrictions of continuous functions
| dc.creator | Kahane, Jean-Pierre | |
| dc.creator | Katznelson, Yitzhak | |
| dc.date | 2007-11-05 | |
| dc.date.accessioned | 2026-07-07T08:45:34Z | |
| dc.date.available | 2026-07-07T08:45:34Z | |
| dc.description | Given a continuous real-valued function on [0, 1], and a closed subset E \subset [0, 1] we denote by f E the restriction of f to E, that is, the function defined only on E that takes the same values as f at every point of E >. The restriction f E will typically be "better behaved" than f . It may have bounded variation when f doesn't, it may have a better modulus of continuity than f, it may be monotone when f is not, etc. All this clearly depends on f and on E, and the questions that we discuss here are about the existence, for every f, or every f in some class, of "substantial" sets E such that f E has bounded total variation, is monotone, or satisfies a given modulus of continuity. The notion of "substantial" that we use is that of either Hausdorff or Minkowski dimensions. | |
| dc.description | Article soumis à Israel Journal of Mathematics | |
| dc.identifier | https://arxiv.org/abs/0711.0679 | |
| dc.identifier | http://arxiv.org/abs/0711.0679 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143001 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 26A15, 26A16, 26A45, 26A48 | |
| dc.title | Restrictions of continuous functions | |
| dc.type | text |