Applications of the Projective Limit Functor to Convolution and Partial Differential Equations

Abstract

Let e {ω{(ℝ N ) denote the non-quasianalytic class of all {ω{-ultradifferentiable functions on ℝ N . This notion is an extension of the classical Gevrey classes Γ{d{(ℝ N ), d > 1. Reporting on our work [5] and [6], we explain how the projective limit functor introduced by Palamodov [21] can be used to characterize the surjectivity of (1) convolution operators T μ on e {ω{(ℝ) and (2) linear partial differential operators P(D) on e {ω{(ℝ N ).