Large eigenvalues and trace formulas for matrix Sturm-Liouville problems

This work describes the location of large eigenvalues for Sturm-Liouville operators with matrix coefficients. Eigenvalue asymptotics of arbitrary order are characterized for operators with smooth coefficients and "elementary" boundary conditions. In addition, an effective method is given for computing traces of these operators. These techniques are employed to verify a previously conjectured trace formula.