The present paper establishes non-asymptotic estimates from above and below on the integrated density of states of the Schrödinger operator L=−Δ+V, using a counting function for the minima of the localization landscape, a solution to the equation Lu=1.
|Original language||English (US)|
|Journal||Advances in Mathematics|
|State||Published - Oct 29 2021|
Bibliographical noteFunding Information:
David is supported in part by the H2020 grant GHAIA 777822, and Simons Foundation grant 601941, GD. Filoche is supported in part by Simons Foundation grant 601944, MF. Mayboroda is supported in part by the NSF grants DMS 1344235, DMS 1839077, and Simons Foundation grant 563916, SM.
- Integrated density of states
- Weyl law