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A Decomposition Theorem for Higher-Order Sturm-Liouville Problems on the Line and Numerical Approximation of the Spectrum

ABSTRACT In this work, we present a decomposition of the scattering matrix for higher-order Sturm-Liouville problems in terms of scattering matrices associated to disjointly supported potentials. Consequently, we propose a numerical method to approximate the eigenvalue problem. It is shown that the theory and numerics apply to the non self-adjoint case.