Exact local distribution of the absolutely continuous spectral measure
Abstract
Abstract It is well‐established that the spectral measure for one‐frequency Schrödinger operators with Diophantine frequencies exhibits optimal ‐Hölder continuity within the absolutely continuous spectrum (Avila and Jitomirskaya, Commun. Math. Phys . 301 (2011), 563–581). This study extends these findings by precisely characterizing the local distribution of the spectral measure for dense small multi‐frequency potentials, including a notable result for any subcritical almost Mathieu operators. Additionally, we investigate the stratified Hölder continuity of the spectral measure at subcritical energies.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Mathematical Analysis and Transform Methods
Numerical methods in inverse problems
Publication details
- Journal / source
- Proceedings of the London Mathematical Society
- Volume
- 132
- Issue
- 4
- Publication date
- 1 April 2026
- Language
- EN