Electron. J. Diff. Eqns., Vol. 2000(2000), No. 55, pp. 1-8.
### A generalization of Gordon's theorem and applications to quasiperiodic
Schrodinger operators

David Damanik & Gunter Stolz

**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.
Submitted May 12, 2000. Published July 18, 2000.

Math Subject Classifications: 34L05, 34L40, 81Q10.

Key Words: Schrodinger operators, eigenvalue problem, quasiperiodic potentials.

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David Damanik

Department of Mathematics 253-37, California Institute of Technology

Pasadena, CA 91125, USA

and Fachbereich Mathematik, Johann Wolfgang Goethe-Universitat

60054 Frankfurt, Germany

e-mail: damanik@its.caltech.edu
Gunter Stolz

Department of Mathematics, University of Alabama at Birmingham

Birmingham, AL 35294, USA

e-mail: stolz@math.uab.edu

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