Lower bounds for quasianalytic functions, II. The Bernstein quasianalytic functions

dc.creatorBorichev, Alexander
dc.creatorNazarov, Fedor
dc.creatorSodin, Mikhail
dc.date2003-01-20
dc.date2003-01-21
dc.date.accessioned2026-07-07T06:30:20Z
dc.date.available2026-07-07T06:30:20Z
dc.descriptionLet 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.identifierhttps://arxiv.org/abs/math/0301217
dc.identifierhttp://arxiv.org/abs/math/0301217
dc.identifierMath. Scand. 95 (2004), 44--58.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/98315
dc.subjectClassical Analysis and ODEs
dc.titleLower bounds for quasianalytic functions, II. The Bernstein quasianalytic functions
dc.typetext

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