Renormalized Oscillation Theory for Singular Linear Hamiltonian Systems

Abstract

Working with a general class of linear Hamiltonian systems with at least one singular boundary condition, we show that renormalized oscillation results can be obtained in a natural way through consideration of the Maslov index associated with appropriately chosen paths of Lagrangian subspaces of ${\mathbb{C}}^{2n}$. This extends previous work by the authors for regular linear Hamiltonian systems.

55 pages, 2 figures