Spectral study of a self-adjoint operator on $L^2 (\Omega )$ related with a Poincaré type constant

Maurice Gaultier; Mikel Lezaun

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L’auteur reprend l’étude classique de la représentation spectrale d’un opérateur auto-adjoint $A$ dans un espace de Hilbert $ℋ$ . Il y ajoute des précisions nouvelles qui conduisent à la définition du projecteur infinitésimal $P^{) λ)}$ sur l’espace des vecteurs propres généralisés $ℋ^{(λ)}$ . Il obtient, par conséquent, des énoncés plus précis de bien des théorèmes classiques. Il introduit ensuite la notion de “ $A$ -expansibilité” d’un sous-ensemble $S \subset ℋ$ . Cette notion est appliquée à l’étude des espaces fonctionnels...

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Displaying similar documents to “Spectral study of a self-adjoint operator on L 2 ( Ω ) related with a Poincaré type constant”

Displaying similar documents to “Spectral study of a self-adjoint operator on $L^{2} (Ω)$ related with a Poincaré type constant”