A Real Analytic Schwartz’ Kernels Theorem
Institut de Mathématique (Bât B37),Université de Liège, Allée des Chevreuils, 4000 Liège (Sart-Tilman), BELGIQUE, jpschneiders@ulg.ac.be
Abstract
In this short paper, we study a few topological properties of the sheaf of real analytic functions on a real analytic manifold M. In particular, we show that its topological Poincaré-Verdier dual is the sheaf of hyperfunction densities on M. We also prove that if N is a second real analytic manifold, then the continuous cohomological correspondences between the sheaf of real analytic functions on M and the sheaf of hyperfunctions on N are given by integral transforms whose kernels are hyperfunction forms on M N of a suitable kind. This result may be viewed as a real analytic analogue of the well-known kernels theorem of Schwartz.