  Quasianalytic classes are classes of infinitely differentiable functions that
satisfy the analytic continuation property enjoyed by analytic functions. Two
general examples are quasianalytic Denjoy-Carleman classes (of origin in the
analysis of linear partial differential equations) and the class of infinitely
differentiable functions that are definable in a polynomially bounded o-minimal
structure (of origin in model theory). We prove a generalization to
quasianalytic functions of Malgrange's celebrated theorem on the division of
infinitely differentiable by real-analytic functions.
