Damanik, David and Stolz, Günter (2000) A generalization of Gordon's theorem and applications to quasiperiodic Schrodinger operators. Electronic Journal of Differential Equations, 2000 (55). pp. 1-8. ISSN 1072-6691. https://resolver.caltech.edu/CaltechAUTHORS:DAMejde00
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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.
| Item Type: | Article | |||||||||
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| Additional Information: | © 2000 Southwest Texas State University and University of North Texas. Submitted May 12, 2000. Published July 18, 2000. (D.D.) Supported by the German Academic Exchange Service through Hochschulsonderprogramm III (Postdoktoranden). (G.S.) Partially supported by NSF Grant DMS 9706076. | |||||||||
| Subject Keywords: | Schrodinger operators, eigenvalue problem, quasiperiodic potentials | |||||||||
| Issue or Number: | 55 | |||||||||
| Classification Code: | Math Subject Classifications: 34L05, 34L40, 81Q10 | |||||||||
| Record Number: | CaltechAUTHORS:DAMejde00 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:DAMejde00 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 4118 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Archive Administrator | |||||||||
| Deposited On: | 28 Jul 2006 | |||||||||
| Last Modified: | 18 May 2020 15:56 |
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