Lower bounds for quasianalytic functions, II. The Bernstein quasianalytic functions
| dc.creator | Borichev, Alexander | |
| dc.creator | Nazarov, Fedor | |
| dc.creator | Sodin, Mikhail | |
| dc.date | 2003-01-20 | |
| dc.date | 2003-01-21 | |
| dc.date.accessioned | 2026-07-07T06:30:20Z | |
| dc.date.available | 2026-07-07T06:30:20Z | |
| dc.description | Let F be a class of functions with the uniqueness property: if a function f in F vanishes on a set of positive measure, then f is the zero function. In many instances, we would like to have a quantitative version of this property, e.g. a lower bound for |f| outside a small exceptional set. Such estimates are well-known and useful for polynomials, complex- and real-analytic functions, exponential polynomials. In this work we prove similar results for the Denjoy-Carleman and the Bernstein classes of quasianalytic functions. In the first part (this arXiv:math.CA/0208233), we considered quasianalytically smooth functions. Here, we deal with classes of functions characterized by exponentially fast approximation by polynomials whose degrees belong to a given very lacunar sequence. We also prove the polynomial spreading lemma and a comparison lemma which are of a certain interest on their own. | |
| dc.identifier | https://arxiv.org/abs/math/0301217 | |
| dc.identifier | http://arxiv.org/abs/math/0301217 | |
| dc.identifier | Math. Scand. 95 (2004), 44--58. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/98315 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.title | Lower bounds for quasianalytic functions, II. The Bernstein quasianalytic functions | |
| dc.type | text |