A boundary-value problem for an ordinary differential equation whose coefficients are in a B*-algebra

SynopsisWe give some results on a boundary-value problem for an ordinary differential equation whose coefficients are in the B*-algebra C(K), where K is a compact metric space. We deduce the existence of a countable number of eigenvalues and corresponding eigenfunctions, the latter being complete in a certain sense. There follows an expansion result and some remarks on a self-adjoint realisation of the associated differential operator.