Oscillation criterion for discrete trigonometric systems
| Authors | |
|---|---|
| Year of publication | 2015 |
| Type | Article in Periodical |
| Magazine / Source | J. Difference Equ. Appl. |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1080/10236198.2015.1070842 |
| Field | General mathematics |
| Keywords | Trigonometric system; oscillation criterion; focal points; symplectic SVD; comparative index |
| Attached files | |
| Description | In this paper we investigate oscillation properties of discrete trigonometric systems whose coefficients matrices are simultaneously symplectic and orthogonal. The main result generalizes a necessary and sufficient condition of nonoscillation of trigonometric systems proved by M.~Bohner and O.~Do\v{s}l\'y (J. Differential Equations 163 (2000), 113--129) in the case when the block in the upper right corner of the coefficient matrix is symmetric and positive definite. Now we present this oscillation criterion for an arbitrary trigonometric system. The obtained results are applied to formulate a necessary and sufficient condition for nonoscillation of even-order Sturm-Liouville difference equations |
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