Spectral inequalities for Schrödinger equations with various potentials
Abstract
We study the spectral inequalities of Schrödinger operators in the whole space for different potentials, which can be polynomial type growth or bounded potentials. The spectral inequalities quantitatively depend on the density of the sensor sets with positive measure, growth rate of the potentials and spectrum (or eigenvalues). One important component in the proof is the adaptation of propagation of smallness argument for gradients by Logunov and Malinnikova [ Proceedings of the International Congress of Mathematicians—Rio de Janeiro 2018. Vol. III. Invited Lectures , World Sci. Publ., Hackensack, NJ, pp. 2391–2411]. As an application, we apply the spectral inequalities to obtain quantitative observability inequalities for heat equations.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Numerical methods in inverse problems
Differential Equations and Boundary Problems
Publication details
- Journal / source
- Transactions of the American Mathematical Society
- Volume
- 379
- Issue
- 8
- Pages
- 5683–5712
- Publication date
- 14 April 2026
- Language
- EN