Weyl-Titchmarsh theory for discrete symplectic systems with general linear dependence on spectral parameter

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Authors

ŠIMON HILSCHER Roman ZEMÁNEK Petr

Year of publication 2014
Type Article in Periodical
Magazine / Source Journal of Difference Equations and Applications
MU Faculty or unit

Faculty of Science

Citation
Doi http://dx.doi.org/10.1080/10236198.2013.813496
Field General mathematics
Keywords Weyl-Titchmarsh theory; symplectic system; M-function; Weyl disk; Weyl circle; limit point case; limit circle case; square summable solution
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Description In this paper we develop the Weyl-Titchmarsh theory for discrete symplectic systems with general linear dependence on the spectral parameter. We generalize and complete several recent results concerning these systems, which have the spectral parameter only in the second equation. Our new theory includes characterizations of the Weyl disks and Weyl circles, their limiting behavior, properties of square summable solutions including the analysis of the exact number of linearly independent square summable solutions, and limit point/circle criteria. Some illustrative examples are also provided.
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