On Dirichlet-integrable solutions of left-definite Hamiltonian systems

This paper aims to share a method to handle left-definite Hamiltonian systems and to construct nested-ellipsoids related with the corresponding hermitian forms. We share a lower bound for the number of linearly independent Dirichlet-integrable solutions of the Hamiltonian systems with respect to some nonnegative matrices. Moreover, we share the corresponding Titchmarsh-Weyl functions. At the end of the paper we introduce a limit-point criterion.