
On the Essential Self-Adjointness of Singular Sub-Laplacians
Franceschi, Valentina; Prandi, Dario; Rizzi, Luca (2019), On the Essential Self-Adjointness of Singular Sub-Laplacians, Potential Analysis, 53, p. 89-112. 10.1007/s11118-018-09760-w
View/ Open
Type
Article accepté pour publication ou publiéDate
2019Journal name
Potential AnalysisVolume
53Publisher
Step Communications
Pages
89-112
Publication identifier
Metadata
Show full item recordAuthor(s)
Franceschi, ValentinaLaboratoire de Mathématiques d'Orsay [LM-Orsay]
Centre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
Prandi, Dario

CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Laboratoire des signaux et systèmes [L2S]
Rizzi, Luca

Institut Fourier [IF ]
Abstract (EN)
We prove a general essential self-adjointness criterion for sub-Laplacians on complete sub-Riemannian manifolds, defined with respect to singular measures. We also show that, in the compact case, this criterion implies discreteness of the sub-Laplacian spectrum even though the total volume of the manifold is infinite. As a consequence of our result, the intrinsic sub-Laplacian (i.e. defined w.r.t. Popp’s measure) is essentially self-adjoint on the equiregular connected components of a sub-Riemannian manifold. This settles a conjecture formulated by Boscain and Laurent (Ann. Inst. Fourier (Grenoble) 63(5), 1739–1770, 2013), under mild regularity assumptions on the singular region, and when the latter does not contain characteristic points.Subjects / Keywords
Sub-Laplacian; Hörmander-type operators; Singular measure; Popp’s measure; Quantum confinementRelated items
Showing items related by title and author.
-
Pizzichillo, Fabio; Bosch, Hanne Van Den (2021) Article accepté pour publication ou publié
-
Esteban, Maria J.; Loss, Michael (2008) Communication / Conférence
-
Esteban, Maria J.; Loss, Michael (2007) Article accepté pour publication ou publié
-
Lehtonen, Erkko; Couceiro, Miguel (2007) Article accepté pour publication ou publié
-
Parini, Enea; Grumiau, Christopher (2008) Article accepté pour publication ou publié