English

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

Classical Analysis and ODEs 2021-12-14 v2

Abstract

Working with a general class of linear Hamiltonian systems on [0,1][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 C2n\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.

Keywords

Cite

@article{arxiv.1808.08264,
  title  = {Renormalized oscillation theory for linear Hamiltonian systems on [0,1] via the Maslov index},
  author = {Peter Howard and Alim Sukhtayev},
  journal= {arXiv preprint arXiv:1808.08264},
  year   = {2021}
}