Copyright © 2010 Shurong Sun et al. This is an open access article distributed under the
Creative 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 , 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.