A Generalization of Gordon's Theorem and Applications to Quasiperiodic Schrodinger Operators

Date

2000-07-18

Authors

Damanik, David
Stolz, Gunter

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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.

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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.

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Attribution 4.0 International

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