Horst Behncke

The absolutely continuous spectrum of a very general class of differential operators of order $2n$ is determined, for operators whose coefficients satisfy conditions that combine smoothness and decay properties. The main methods are asymptotic integration and the analysis of the associated $M$-matrix. The form of the solutions precludes the absence of a singular continuous spectrum.

2000 Mathematics Subject Classification: 34L05, 47E05.

Keywords: absolutely continuous spectrum, $M$-matrix, asymptotic integration.