Quantitative spectral inequalities for the anisotropic Shubin operators and applications to null-controllability (Q6644096)

In this work, the authors establish quantitative spectral inequalities for (anisotropic) Shubin operators on Euclidean space, relating the \(L^2\)-norm on the whole space to the \(L^2\)-norm on subsets. The estimates feature explicit constants dependent on geometric parameters of subsets, which may be sparse at infinity or have finite measure. These results extend recent work by J. Martin and, for the harmonic oscillator, by A. Dicke, I. Veselić, and the second author. Applications include null-controllability of associated parabolic equations and Baouendi-Grushin operators on \(\mathbb{R}^d \times \mathbb{T}^d\).