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Symplectic Difference Systems: Oscillation and Spectral Theory

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  • © 2019

Overview

Authors:
  1. Ondřej Došlý

    1. Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Brno, Czech Republic

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  2. Julia Elyseeva

    1. Department of Applied Mathematics, Moscow State Technological University “STANKIN”, Moscow, Russia

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    You can also search for this author in PubMed   Google Scholar

  3. Roman Šimon Hilscher

    1. Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Brno, Czech Republic

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    You can also search for this author in PubMed   Google Scholar

  • First monograph on symplectic difference systems
  • Novel approach to discrete oscillation and spectral theory via the comparative index
  • Provides numerous results and citations scattered in many journals

Part of the book series: Pathways in Mathematics (PATHMATH)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xv
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  2. Motivation and Preliminaries

    • Ondřej Došlý, Julia Elyseeva, Roman Šimon Hilscher
    Pages 1-81

  3. Basic Theory of Symplectic Systems

    • Ondřej Došlý, Julia Elyseeva, Roman Šimon Hilscher
    Pages 83-148

  4. Comparative Index Theory

    • Ondřej Došlý, Julia Elyseeva, Roman Šimon Hilscher
    Pages 149-200

  5. Oscillation Theory of Symplectic Systems

    • Ondřej Došlý, Julia Elyseeva, Roman Šimon Hilscher
    Pages 201-260

  6. Discrete Symplectic Eigenvalue Problems

    • Ondřej Došlý, Julia Elyseeva, Roman Šimon Hilscher
    Pages 261-396

  7. Miscellaneous Topics on Symplectic Systems

    • Ondřej Došlý, Julia Elyseeva, Roman Šimon Hilscher
    Pages 397-572

  8. Back Matter

    Pages 573-593
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Brno, Czech Republic

    Ondřej Došlý, Roman Šimon Hilscher

  • Department of Applied Mathematics, Moscow State Technological University “STANKIN”, Moscow, Russia

    Julia Elyseeva

Bibliographic Information

  • Book Title: Symplectic Difference Systems: Oscillation and Spectral Theory

  • Authors: Ondřej Došlý, Julia Elyseeva, Roman Šimon Hilscher

  • Series Title: Pathways in Mathematics

  • DOI: https://doi.org/10.1007/978-3-030-19373-7

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2019

  • Hardcover ISBN: 978-3-030-19372-0Published: 20 September 2019

  • Softcover ISBN: 978-3-030-19375-1Published: 20 September 2020

  • eBook ISBN: 978-3-030-19373-7Published: 06 September 2019

  • Series ISSN: 2367-3451

  • Series E-ISSN: 2367-346X

  • Edition Number: 1

  • Number of Pages: XV, 593

  • Number of Illustrations: 7 illustrations in colour

  • Topics: Difference and Functional Equations, Operator Theory

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