Critères de Complétude des Vecteurs Propres Généralisés d'une Classe d'Opérateurs Non Auto-adjoints Compacts ou à Résolvante Compacte et Applications

Abstract

In this work we establish sufficient conditions on thé denseness of thé generalized eigenvectors for a class of compact (or compact résolvent) non self adjoint operators. We can apply our results to operators arising in many fields, particularly in field's theory and in abstract second order differential équations. Our results generalize some results of Aimar and al [1] and [2], Macaev and Keldysh [11] and Dunford-Schwartz [9].