AWeak Gordon Type Condition for Absence of Eigenvalues of One-dimensional Schr?dinger Operators

摘要

We study one-dimensional Schr?dinger 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.