Symmetric three-term recurrence equations and their symplectic structure
| Authors | |
|---|---|
| Year of publication | 2010 |
| Type | Article in Periodical |
| Magazine / Source | Advances in Difference Equations |
| MU Faculty or unit | |
| Citation | |
| Field | General mathematics |
| Keywords | Three-term recurrence equation; Discrete symplectic system; Discrete Jacobi equation; linear Hamiltonian system; Quadratic functional |
| Description | In this paper we revive the study of the symmetric three-term recurrence equations. Our main result shows that these equations have a natural symplectic structure, that is, every symmetric three-term recurrence equation is a special discrete symplectic system. The assumptions on the coefficients in this paper are weaker and more natural than those in the current literature. In addition, our result implies that symmetric three-term recurrence equations are completely equivalent with Jacobi difference equations arising in the discrete calculus of variations. Presented applications of this study include the Riccati equation and inequality, detailed Sturmian separation and comparison theorems, and the eigenvalue theory for these three-term recurrence and Jacobi equations. |
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