Work

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

Year: 2024

Type: article

Abstract: 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. Veselić, 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 ℝ d × 𝕋 d .

Source: Comptes Rendus Mathématique

DOI: 10.5802/crmath.670

Authors: Paul Alphonse, Albrecht Seelmann

Institutions: École Normale Supérieure de Lyon, Unité de Mathématiques Pures et Appliquées, TU Dortmund University, Université de Lyon

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Deutsche Forschungsgemeinschaft

Award: G7938957394