Geodesic
A generalization of Gordon's theorem and applications to quasiperiodic Schrödinger operators
Electronic journal of differential equations, Tome 2000 (2000)
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},
     year = {2000},
     volume = {2000},
     zbl = {0954.34074},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a89/}
}
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AU  - Stolz,  Günter
TI  - A generalization of Gordon's theorem and applications to quasiperiodic Schrödinger operators
JO  - Electronic journal of differential equations
PY  - 2000
VL  - 2000
UR  - http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a89/
LA  - en
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%A Damanik,  David
%A Stolz,  Günter
%T A generalization of Gordon's theorem and applications to quasiperiodic Schrödinger operators
%J Electronic journal of differential equations
%D 2000
%V 2000
%U http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a89/
%G en
%F EJDE_2000__2000__a89
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/