Electronic Journal of Differential Equations,
Vol. 2000(2000), No. 55, pp. 1-8.

Title: A generalization of Gordon's theorem and applications to quasiperiodic 
       Schrodinger operators

Authors:  David Damanik (California Inst. of Technology, Pasadena, CA, USA)
          Gunter Stolz (University of Alabama at Birmingham, USA)
         
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.