Critères de Complétude des Vecteurs Propres Généralisés d'une Classe d'Opérateurs Non Auto-adjoints Compacts ou à Résolvante Compacte et Applications
Copyright policy )Critères de Complétude des Vecteurs Propres Généralisés d'une Classe d'Opérateurs Non Auto-adjoints Compacts ou à Résolvante Compacte et Applications
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].
- Aix-Marseille University France
Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.), General theory of partial differential operators, Completeness of eigenfunctions and eigenfunction expansions in context of PDEs, compact resolvent, denseness of the generalized eigenvectors, self adjoint operators, field theory, abstract second order differential equations, Linear symmetric and selfadjoint operators (unbounded), Eigenvalue problems for linear operators, Linear operators defined by compactness properties, Spectrum, resolvent, (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces
Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.), General theory of partial differential operators, Completeness of eigenfunctions and eigenfunction expansions in context of PDEs, compact resolvent, denseness of the generalized eigenvectors, self adjoint operators, field theory, abstract second order differential equations, Linear symmetric and selfadjoint operators (unbounded), Eigenvalue problems for linear operators, Linear operators defined by compactness properties, Spectrum, resolvent, (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces
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