Quantitative spectral inequalities for the anisotropic Shubin operators and applications to null-controllability - ENS de Lyon - École normale supérieure de Lyon Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

Quantitative spectral inequalities for the anisotropic Shubin operators and applications to null-controllability

Paul Alphonse
  • Fonction : Auteur
  • PersonId : 1037204
Albrecht Seelmann
  • Fonction : Auteur
  • PersonId : 1208773

Résumé

We prove quantitative spectral inequalities for the (anisotropic) Shubin operators on the whole Euclidean space, thus relating for functions from spectral subspaces associated to finite energy intervals their $L^2$-norm on the whole space to the $L^2$-norm on a suitable subset. A particular feature of our estimates is that the constant relating these $L^2$-norms is very explicit in geometric parameters of the corresponding subset of the whole space, which may become sparse at infinity and may even have finite measure. This extends results obtained recently by J. Martin and, in the particular case of the harmonic oscillator, by A. Dicke, I. Veseli\'c, and the second author. We apply our results towards null-controllability of the associated parabolic equations, as well as to the ones associated to the (degenerate) Baouendi-Grushin operators acting on $\mathbb R^d \times \mathbb T^d$.
Fichier principal
Vignette du fichier
GeneralSpeEstimates__2023_04_05.pdf (400.49 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03908252 , version 1 (20-12-2022)
hal-03908252 , version 2 (20-04-2023)
hal-03908252 , version 3 (18-12-2023)

Identifiants

  • HAL Id : hal-03908252 , version 2

Citer

Paul Alphonse, Albrecht Seelmann. Quantitative spectral inequalities for the anisotropic Shubin operators and applications to null-controllability. 2023. ⟨hal-03908252v2⟩
22 Consultations
22 Téléchargements

Partager

Gmail Facebook X LinkedIn More