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For Hill's equation on [0,infinity) we prove new characterizations of thespectral function rho(lambda) and the spectral density function f(lambda) basedon analysis involving a companion system of first order differential equationsin [6,7]. A numerical algorithm is derived and implemented based on coefficientapproximation. Results for several examples, including the Mathieu equation,are presented.

Algorithms for estimating spectral density functions for periodic potentials on the half line