doi:10.1155/2010/514760 Research Article Weyl-Titchmarsh Theory for Hamiltonian Dynamic Systems

Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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 Mλ theory for singular Hamiltonian systems, ii on the spectrum of Hamiltonian systems, iii on boundary value problems for Hamiltonian dynamic systems. 1