This paper
gives one-term componentwise asymptotics for the $M$ and spectral matrices of a self-adjoint realisation of an
even-order ordinary differential expression. The underlying interval is assumed to have at least one regular
endpoint, and the boundary conditions are supposed to be separated. Furthermore, the weight function and the
reciprocal of the highest-order coefficient are supposed to be of regular variation at the regular
endpoint, in the sense of Bingham, Goldie and Teugels.
1991 Mathematics Subject Classification: 34B24,
34E05.