Weyl-Titchmarsh Theory for Hamiltonian Dynamic Systems

Shurong Sun, Martin Bohner and Shaozhu Chen

Abstract and Applied Analysis, 2010, vol. 2010, 1-18

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.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:514760

DOI: 10.1155/2010/514760

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