New Results in Theory of Symplectic Systems on Time Scales
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| Year of publication | 2011 |
| Type | Monograph |
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| Description | We present new results in the theory of symplectic systems on time scales obtained and published by the author (jointly with collaborators) during his doctoral study between the years 2007 and 2011. The book is organized into five chapters. The study of symplectic systems is motivated in the introductory chapter, where an overview of the new results contained in the text is also given. In the second chapter, the reader will find fundamental parts of the time scale calculus. In Chapter 3, we define trigonometric and hyperbolic systems on time scales and study their properties. In the following Chapter 4, the Weyl–Titchmarsh theory for symplectic dynamic systems is established. The theory given in both of these chapters is new even for symplectic difference systems. In the final chapter, we pay our attention to the study of the second order Sturm-Liouville equations on time scales, especially to the Krein–von Neumann and Friedrichs extensions and to the concept of the critical operators. |
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