The Maslov Index and Spectral Counts for Linear Hamiltonian Systems on [0,1]

摘要

Working with general linear Hamiltonian systems on [ 0, 1], and with a wide range of self-adjoint boundary conditions, including both separated and coupled, we develop a general framework for relating the Maslov index to spectral counts. Our approach is illustrated with applications to Schrodinger systems on R with periodic coefficients, and to EulerBernoulli systems in the same context.