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

F. Nazarov·M. Sodin·A. Volberg
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Abstract

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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F. Nazarov, M. Sodin, A. Volberg. 2003-01-20. Lower bounds for quasianalytic functions, I. How to control smooth functions?. https://arxiv.org/abs/math/0208233

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