Sturmian and Spectral Theory for Discrete Symplectic Systems

Abstract

We consider 2n x 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.

Department(s)

Mathematics and Statistics

Keywords and Phrases

discrete symplectic system; disrete quadratic functional; Sturmian separation result; Sturmian comparison result; Rayleigh principle; extended Picone identity

International Standard Serial Number (ISSN)

0002-9947

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2009 American Mathematical Society, All rights reserved.

Publication Date

01 Jan 2009

Link to Full Text

Share

 
COinS