Equidistribution estimates for eigenfunctions and eigenvalue bounds for random operators

Abstract

We discuss properties of $L^2$-eigenfunctions of Schrödinger operators and elliptic partial differential operators. The focus is set on unique continuation principles and equidistribution properties. We review recent results and announce new ones.

Keywords: scale-free unique continuation property, equidistribution property, observability estimate, uncertainty relation, Carleman estimate, Schrödinger operator, elliptic differential equation

Cited by in corpus (1)

• A quantitative Carleman estimate for second order elliptic operators