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International Conference on Difference Equations and Applications

ICDEA 2019: Progress on Difference Equations and Discrete Dynamical Systems pp 435–448Cite as

Linear Operators Associated with Differential and Difference Systems: What Is Different?

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Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS,volume 341)

Abstract

The existence of a densely defined operator associated with (time-reversed) discrete symplectic systems is discussed and the necessity of the development of the spectral theory for these systems by using linear relations instead of operators is shown. An explanation of this phenomenon is provided by using the time scale calculus. In addition, the density of the domain of the maximal linear relation associated with the system is also investigated.

Keywords

  • Discrete symplectic system
  • Linear hamiltonian differential system
  • Linear relations
  • Multi-valuedness
  • Densely defined operator
  • Time scale

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Acknowledgements

The research was supported by the Czech Science Foundation under Grant GA16-00611S. The author is grateful to the anonymous referee for a detailed reading of the manuscript and her/his comments.

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Authors and Affiliations

  1. Faculty of Science, Department of Mathematics and Statistics, Masaryk University, Kotlářská 2, 61137, Brno, Czech Republic

    Petr Zemánek

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  1. Petr Zemánek
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Correspondence to Petr Zemánek .

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Editors and Affiliations

  1. Department of Mathematics, University College London, London, UK

    Dr. Steve Baigent

  2. Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO, USA

    Martin Bohner

  3. Department of Mathematics, Trinity University, San Antonio, TX, USA

    Prof. Dr. Saber Elaydi

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Zemánek, P. (2020). Linear Operators Associated with Differential and Difference Systems: What Is Different?. In: Baigent, S., Bohner, M., Elaydi, S. (eds) Progress on Difference Equations and Discrete Dynamical Systems. ICDEA 2019. Springer Proceedings in Mathematics & Statistics, vol 341. Springer, Cham. https://doi.org/10.1007/978-3-030-60107-2_25

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