Lower bounds for quasianalytic functions, I. How to control smooth functions?

Details Lower bounds for quasianalytic functions, I. How to control smooth functions? Lower bounds for quasianalytic functions, I. How to control smooth functions?

2002-08-29

arxiv.org/abs/math/0208233v2

Math. Scand. 95 (2004), 59--79.

Mathematics

Classical Analysis and ODEs

Stylistic corrections have been made

Scientific paper

Consider a class of functions of one real variable with the following uniqueness property: if a function f(x) from the class 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(x) outside a small exceptional set. Such estimates are well-known and useful for polynomials and analytic functions. In this work we prove similar results for the Denjoy-Carleman and the Bernstein classes of quasianalytic functions.

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