Renormalized oscillation theory for linear Hamiltonian systems on [0,1] via the Maslov index

Abstract

Working with a general class of linear Hamiltonian systems on $[0,1]$, 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 ${\mathbb{C}}^{2n}$. We verify that our applicability class includes Dirac and Sturm-Liouville systems, as well as a system arising from differential-algebraic equations for which the spectral parameter appears nonlinearly.

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