Spectral theory and stability in astrophysics

This paper is part II of a limited review of the applications of the spectral theory of linear operators in an astrophysical context. A major part of the paper is devoted to describing the results obtained by Dyson and Schutz (1979) for differentially rotating perfect fluid stars. The functional-analytic techniques used and the results so obtained are compared with those in Paper I. As in the case of ideal magnetohydrodynamics, the mathematical structure of the rotating star problem is very rich indeed. Many questions remain unanswered in both areas.