We establish the Weyl-Titchmarsh theory for singular linear Hamiltonian dynamic systems on a time scale , which allows one to treat both continuous and discrete linear Hamiltonian systems as special cases for and 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) theory for singular Hamiltonian systems, (ii) on the spectrum of Hamiltonian systems, (iii) on boundary value problems for Hamiltonian dynamic systems.
Shurong Sun. Martin Bohner. Shaozhu Chen. "Weyl-Titchmarsh Theory for Hamiltonian Dynamic Systems." Abstr. Appl. Anal. 2010 1 - 18, 2010. https://doi.org/10.1155/2010/514760