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Weyl-Titchmarsh Theory for Hamiltonian Dynamic Systems

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  • Shurong Sun
  • Martin Bohner
  • Shaozhu Chen

Abstract

We establish the Weyl-Titchmarsh theory for singular linear Hamiltonian dynamic systems on a time scale 𝕋 , which allows one to treat both continuous and discrete linear Hamiltonian systems as special cases for 𝕋 = â„ and 𝕋 = ℤ within one theory and to explain the discrepancies between these two theories. This paper extends the Weyl-Titchmarsh theory and provides a foundation for studying spectral theory of Hamiltonian dynamic systems. These investigations are part of a larger program which includes the following: (i) M ( λ ) theory for singular Hamiltonian systems, (ii) on the spectrum of Hamiltonian systems, (iii) on boundary value problems for Hamiltonian dynamic systems.

Suggested Citation

  • Shurong Sun & Martin Bohner & Shaozhu Chen, 2010. "Weyl-Titchmarsh Theory for Hamiltonian Dynamic Systems," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-18, March.
    • Handle: RePEc:hin:jnlaaa:514760
    DOI: 10.1155/2010/514760
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    Cited by:

    1. Huseynov, Adil, 2011. "Existence of a spectral measure for second-order delta dynamic equations on semi-infinite time scale intervals," Chaos, Solitons & Fractals, Elsevier, vol. 44(9), pages 769-777.

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