Fáze a oscilační teorie diferenčních rovnic druhého řádu

Mgr. Šárka Pechancová, Ph.D.

Doctoral thesis

Phases and Oscillation Theory of Second Order Difference Equations

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

Language used: English

Date on which the thesis was submitted / produced: 25. 5. 2007

Thesis defence

• Date of defence: 25. 5. 2007
• Supervisor: prof. RNDr. Zuzana Došlá, DSc.

Masaryk University

Faculty of Science

Doctoral programme / field:
Mathematics / Mathematical Analysis