Weyl-Titchmarsh Theory for Hamiltonian Dynamic Systems

Abstract EN

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 ?=ℝ and ?=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.