As is well known, the classical Titchmarsh–Weyl m-function
for second order differential operators
admits a generalisation to considerably larger classes of differential
equations. In the applications,
however, the use of the general M-matrix often turns out to be
rather cumbersome. The paper interprets
the m-function in terms of Hilbert space notions, and shows that,
in a sense that is made precise, the
classical m-function can be recovered as a part of the more complicated
one. Applications of this trick lead
to results on spectral multiplicity and on stability properties of the
spectrum.