Weyl-Titchmarsh theory for discrete symplectic systems with general linear dependence on spectral parameter
| Authors | |
|---|---|
| Year of publication | 2014 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Difference Equations and Applications |
| MU Faculty or unit | |
| 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 |
| Attached files | |
| 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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