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Symplectic Difference Systems: Oscillation and Spectral Theory

  • Ondřej Došlý
  • Julia Elyseeva
  • Roman Šimon Hilscher

Part of the Pathways in Mathematics book series (PATHMATH)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Ondřej Došlý, Julia Elyseeva, Roman Šimon Hilscher
    Pages 1-81
  3. Ondřej Došlý, Julia Elyseeva, Roman Šimon Hilscher
    Pages 83-148
  4. Ondřej Došlý, Julia Elyseeva, Roman Šimon Hilscher
    Pages 149-200
  5. Ondřej Došlý, Julia Elyseeva, Roman Šimon Hilscher
    Pages 201-260
  6. Ondřej Došlý, Julia Elyseeva, Roman Šimon Hilscher
    Pages 261-396
  7. Ondřej Došlý, Julia Elyseeva, Roman Šimon Hilscher
    Pages 397-572
  8. Back Matter
    Pages 573-593

About this book

Introduction

This monograph is devoted to covering the main results in the qualitative theory of symplectic difference systems, including linear Hamiltonian difference systems and Sturm-Liouville difference equations, with the emphasis on the oscillation and spectral theory. As a pioneer monograph in this field it contains nowadays standard theory of symplectic systems, as well as the most current results in this field, which are based on the recently developed central object - the comparative index. The book contains numerous results and citations, which were till now scattered only in journal papers. The book also provides new applications of the theory of matrices in this field, in particular of the Moore-Penrose pseudoinverse matrices, orthogonal projectors, and symplectic matrix factorizations. Thus it brings this topic to the attention of researchers and students in pure as well as applied mathematics.

Keywords

symplectic system riccati difference equation quadratic functional oscillation theorem eigenvalue problem comparative index linear hamiltonian system focal point recessive solution at infinity

Authors and affiliations

  • Ondřej Došlý
    • 1
  • Julia Elyseeva
    • 2
  • Roman Šimon Hilscher
    • 3
  1. 1.Department of Mathematics and Statistics, Faculty of ScienceMasaryk UniversityBrnoCzech Republic
  2. 2.Department of Applied MathematicsMoscow State Technological University “STANKIN”MoscowRussia
  3. 3.Department of Mathematics and Statistics, Faculty of ScienceMasaryk UniversityBrnoCzech Republic

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-19373-7
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-19372-0
  • Online ISBN 978-3-030-19373-7
  • Series Print ISSN 2367-3451
  • Series Online ISSN 2367-346X
  • Buy this book on publisher's site