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Article Dans Une Revue Annales de la Faculté des Sciences de Toulouse. Mathématiques. Année : 2022

On essential-selfadjointness of differential operators on closed manifolds

Yves Colin de Verdìère

Résumé

The goal of this note is to present some arguments leading to the conjecture that a formally self-adjoint differential operator on a closed manifold is essentially self-adjoint if and only if the Hamiltonian flow of its symbol is complete. This holds for differential operators of degree two on the circle, for differential operators of degree one on any closed manifold and for generic Lorentzian Laplacians on surfaces.
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Dates et versions

hal-02540423 , version 1 (11-04-2020)
hal-02540423 , version 2 (30-04-2023)

Identifiants

Citer

Yves Colin de Verdìère, Corentin Le Bihan. On essential-selfadjointness of differential operators on closed manifolds. Annales de la Faculté des Sciences de Toulouse. Mathématiques., 2022, 31 (5), pp.1287--1302. ⟨10.5802/afst.1719⟩. ⟨hal-02540423v2⟩
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