Conceptual

Quasianalytic Classes of Smooth Functions and the Borel Mapping

An expository treatment of quasianalytic classes of infinitely differentiable functions: classes in which, like real-analytic functions, a function is determined on an interval by all its successive derivatives at a single point, though the functions need not be analytic. Covers the classical Denjoy-Carleman classes, the Borel mapping sending a function to its jet of derivatives (its non-surjectivity and monotonicity), and whether these properties extend to quasianalytic classes of functions definable in polynomially bounded o-minimal structures.