A weak Gordon type condition for absence of eigenvalues of one-dimensional Schrödinger operators

Abstract

We study one-dimensional Schrödinger operators with complex measures as potentials and present an improved criterion for absence of eigenvalues which involves a weak local periodicity condition. The criterion leads to sharp quantitative bounds on the eigenvalues. We apply our result to quasiperiodic measures as potentials.

27 pages, 1 figure