2022/05/23 by Jérémy Martin, Jeremy E. Martin, Martin, Jérémy · 2 citations
Computer Science · Engineering · Mathematics · #Analysis of PDEs (math.AP) #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2205.11868
openalex publication_date 2022/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, new spectral inequalities for finite combinations of\neigenfunctions of anisotropic Shubin operators are presented. Given a subset\n\ω and an energy level, we provide an explicit control of the ratio of\nthe L 2 (R d)-norm over the L 2 (\ω)-norm with respect to the energy\nlevel. The proofs are based on recent uncertainty principles holding in\nGelfand-Shilov spaces and Bernstein type estimates deduced from quantitative\nsmoothing effects proved by Paul Alphonse. These spectral inequalities allow to\nderive the null-controllability in any positive time from any control subset\nwith positive Lebesgue measure of evolution equations associated to anisotropic\nShubin operators, except for the harmonic oscillator.\n