Weyl‐Titchmarsh Theory for Hamiltonian Dynamic Systems

Shurong Sun, Martin Bohner and Shaozhu Chen

Abstract and Applied Analysis, 2010, vol. 2010, issue 1

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 = ℝ 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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https://doi.org/10.1155/2010/514760

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2010:y:2010:i:1:n:514760

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