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Jean-·Pierre Schneiders

A Real Analytic Schwartz’ Kernels Theorem

(Volume 70 - Année 2001 — Numéro 4 - 5 - 6)
Article
Open Access

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.

Pour citer cet article

Jean-·Pierre Schneiders, «A Real Analytic Schwartz’ Kernels Theorem», Bulletin de la Société Royale des Sciences de Liège [En ligne], Volume 70 - Année 2001, Numéro 4 - 5 - 6, 395 - 406 URL : https://popups.uliege.be/0037-9565/index.php?id=1931.

A propos de : Jean-·Pierre Schneiders

Institut de Mathématique (Bât B37),Université de Liège, Allée des Chevreuils, 4000 Liège (Sart-Tilman), BELGIQUE, jpschneiders@ulg.ac.be