On discrete symplectic systems: associated maximal and minimal linear relations and nonhomogeneous problems
| Authors | |
|---|---|
| Year of publication | 2015 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Mathematical Analysis and Applications |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1016/j.jmaa.2014.07.015 |
| Field | General mathematics |
| Keywords | discrete symplectic system; time-reversed system; definiteness condition; nonhomogeneous problem; Hilbert space; maximal linear relation; minimal linear relation; deficiency index. |
| Attached files | |
| Description | In this paper we characterize the definiteness of the discrete symplectic system, study a nonhomogeneous discrete symplectic system, and introduce the minimal and maximal linear relations associated with these systems. Fundamental properties of the corresponding deficiency indices, including a relationship between the number of square summable solutions and the dimension of the defect subspace, are also derived. Moreover, a sufficient condition for the existence of a densely defined operator associated with the symplectic system is provided. |
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