Sturmian and spectral theory for discrete symplectic systems
| Authors | |
|---|---|
| Year of publication | 2009 |
| Type | Article in Periodical |
| Magazine / Source | Trans. Amer. Math. Soc. |
| MU Faculty or unit | |
| Citation | |
| Web | http://www.ams.org/tran/2009-361-06 |
| Field | General mathematics |
| Keywords | Discrete symplectic system; discrete quadratic functional; Rayleigh principle; extended Picone identity |
| Description | We consider 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. |
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