## Sturmian and spectral theory for discrete symplectic systems

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- by Martin Bohner, Ondřej Došlý and Werner Kratz PDF
- Trans. Amer. Math. Soc.
**361**(2009), 3109-3123 Request permission

## Abstract:

We consider $2n\times 2n$ symplectic difference systems together with associated discrete quadratic functionals and eigenvalue problems. We establish Sturmian type comparison theorems for the numbers of focal points of conjoined bases of a pair of symplectic systems. Then, using this comparison result, we show that the numbers of focal points of two conjoined bases of one symplectic system differ by at most $n$. In the last part of the paper we prove the Rayleigh principle for symplectic eigenvalue problems and we show that finite eigenvectors of such eigenvalue problems form a complete orthogonal basis in the space of admissible sequences.## References

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## Additional Information

**Martin Bohner**- Affiliation: Department of Mathematics and Statistics and Department of Economics and Finance, Missouri University of Science and Technology, Rolla, Missouri 65401
- MR Author ID: 295863
- ORCID: 0000-0001-8310-0266
**Ondřej Došlý**- Affiliation: Department of Mathematics and Statistics, Masaryk University, CZ-61137, Brno, Czech Republic
**Werner Kratz**- Affiliation: Institut für Angewandte Analysis, Universität Ulm, D-89069 Ulm, Germany
- Received by editor(s): June 20, 2007
- Published electronically: December 30, 2008
- © Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc.
**361**(2009), 3109-3123 - MSC (2000): Primary 39A12, 39A13, 34B24, 49K99
- DOI: https://doi.org/10.1090/S0002-9947-08-04692-8
- MathSciNet review: 2485420