Publication details
Riccati inequality and other results for discrete symplectic systems
| Authors | |
|---|---|
| Year of publication | 2006 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Mathematical Analysis and Applications |
| MU Faculty or unit | |
| Citation | |
| Field | General mathematics |
| Keywords | Discrete symplectic system; Quadratic functional; Nonnegativity; Positivity; Riccati inequality; Riccati equation; Conjoined basis; Sturmian theorem |
| Description | In this paper we establish several new results regarding the positivity and nonnegativity of discrete quadratic functionals F associated with discrete symplectic systems. In particular, we derive (i) the Riccati inequality for the positivity of F with separated endpoints, (ii) a characterization of the nonnegativity of F for the case of general (jointly varying) endpoints, and (iii) several perturbation-type inequalities regarding the nonnegativity of F with zero endpoints. Some of these results are new even for the special case of discrete Hamiltonian systems. |
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