Lecture notes : Spectral properties of non-self-adjoint operators

Sjöstrand, Johannes

Journées équations aux dérivées partielles (2009), article no. 1, 111 p.

Ce texte contient une version légèrement completée de mon cours de 6 heures au colloque d’équations aux dérivées partielles à Évian-les-Bains en juin 2009. Dans la première partie on expose quelques résultats anciens et récents sur les opérateurs non-autoadjoints. La deuxième partie est consacrée aux résultats récents sur la distribution de Weyl des valeurs propres des opérateurs elliptiques avec des petites perturbations aléatoires. La partie III, en collaboration avec B. Helffer, donne des bornes explicites dans le théorème de Gearhardt-Prüss pour des semi-groupes.

This text contains a slightly expanded version of my 6 hour mini-course at the PDE-meeting in Évian-les-Bains in June 2009. The first part gives some old and recent results on non-self-adjoint differential operators. The second part is devoted to recent results about Weyl distribution of eigenvalues of elliptic operators with small random perturbations. Part III, in collaboration with B. Helffer, gives explicit estimates in the Gearhardt-Prüss theorem for semi-groups.

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