Phases and oscillation theory of second order difference equations - Pechancová, Šárka (2007)
In the dissertation thesis we present results about the oscillatory properties of second order linear difference equations and their connection to phases. Namely, we introduce a concept of first and second phases of Sturm-Liouville difference equations (S-L), and we show the relation between both phases and its connection to the oscillatory properties of (S-L). By means of the phase theory and the Riccati equation the conjugacy of (S-L) is studied. We also study some algebraic properties of (S-L), especially connection between second order linear difference equations, 2x2 symplectic systems, three-term recurrence relations and tridiagonal symmetric matrices and their transformations into their trigonometric counterparts.