Weyl-Titchmarsh theory for time scale symplectic systems on half line
| Authors | |
|---|---|
| Year of publication | 2011 |
| Type | Article in Periodical |
| Magazine / Source | Abstract and Applied Analysis |
| MU Faculty or unit | |
| Citation | |
| Web | http://www.hindawi.com/journals/aaa/differential.difference.equations/ |
| Doi | http://dx.doi.org/10.1155/2011/738520 |
| Field | General mathematics |
| Keywords | Time scale; Time scale symplectic system; Weyl-Titchmarsh theory; M(lambda)-function; Lagrange identity; Weyl disk; Weyl circle; Limit point case; Limit circle case; Linear Hamiltonian system; Discrete symplectic system; Eigenvalue problem |
| Attached files | |
| Description | In this paper we develop the Weyl-Titchmarsh theory for time scale symplectic systems. We introduce the M(lambda)-function, study its properties, construct the corresponding Weyl disk and Weyl circle, and establish their geometric structure including the formulas for their center and matrix radii. Similar properties are then derived for the limiting Weyl disk. We discuss the notions of the system being in the limit point or limit circle case and prove several characterizations of the system in the limit point case and one condition for the limit circle case. We also define the Green function for the associated nonhomogeneous system and use its properties for deriving further results for the original system in the limit point or limit circle case. Our work directly generalizes the corresponding discrete time theory obtained recently by S.Clark and P.Zemánek in Applied Mathematics and Computation. |
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