Geodesic
A generalization of Gordon's theorem and applications to quasiperiodic Schrödinger operators
Electronic Journal of Differential Equations, Tome 2000 (2000).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 34L05, 34L40, 81Q10
Keywords: Schrödinger operators, eigenvalue problem, quasiperiodic potentials 
@article{EJDE_2000__2000__a89,
     author = {Damanik, David and Stolz, G\"unter},
     title = {A generalization of {Gordon's} theorem and applications to quasiperiodic {Schr\"odinger} operators},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2000},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a89/}
}
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Damanik, David; Stolz, Günter. A generalization of Gordon's theorem and applications to quasiperiodic Schrödinger operators. Electronic Journal of Differential Equations, Tome 2000 (2000). http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a89/