A Generalization of Gordon's Theorem and Applications to Quasiperiodic Schrodinger Operators
Date
2000-07-18
Authors
Damanik, David
Stolz, Gunter
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
We present a criterion for absence of eigenvalues for one-dimensional Schrodinger operators. This criterion can be regarded as an L^1-version of Gordon's theorem and it has a broader range of application. Absence of eigenvalues is then established for quasiperiodic potentials generated by Liouville frequencies and various types of functions such as step functions, Holder continuous functions and functions with power-type singularities. The proof is based on Gronwall-type a priori estimates for solutions of Schrodinger equations.
Description
Keywords
Schrodinger operators, Eigenvalue problem, Quasiperiodic potentials
Citation
Damanik, D., & Stolz, G. (2000). A generalization of Gordon's theorem and applications to quasiperiodic Schrodinger operators. <i>Electronic Journal of Differential Equations, 2000</i>(55), pp. 1-8.
Rights
Attribution 4.0 International