The spectrum of radial adiabatic stellar oscillations

Abstract

The stability analysis with respect to ‘‘small’’ radial adiabatic perturbations of spherically symmetric stellar equilibrium models which are polytropic with a constant adiabatic index only near the center and the boundary of the star leads to the consideration of a class of singular minimal Sturm–Liouville operators. It is shown that the physical boundary conditions choose in a unique way the corresponding Friedrichs extensions. Moreover, all linear self-adjoint extensions of the members of the class are determined and are shown to have a purely discrete spectrum.