Detail publikačního výsledku

Phases and Oscillation Theory of Second Order Difference Equations

PECHANCOVÁ, Š.

Originální název

Phases and Oscillation Theory of Second Order Difference Equations

Anglický název

Phases and Oscillation Theory of Second Order Difference Equations

Druh

Dizertace

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

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

Klíčová slova v angličtině

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

Autoři

PECHANCOVÁ, Š.

Vydáno

01.02.2007

BibTex

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