Publication detail

Phases and Oscillation Theory of Second Order Difference Equations

PECHANCOVÁ, Š.

Original Title

Phases and Oscillation Theory of Second Order Difference Equations

Type

dissertation

Language

English

Original Abstract

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.

Keywords

Sturm-Liouville difference equation, Symplectic difference system, Phase, Generalized zero, Conjugacy, Trigonometric symplectic system, Trigonometric recurrence relation, Trigonometric matrix

Authors

PECHANCOVÁ, Š.

Released

1. 2. 2007

BibTex

@phdthesis{BUT66833,
  author="Šárka {Pechancová}",
  title="Phases and Oscillation Theory of Second Order Difference Equations",
  year="2007"
}