Spectral theory and stability in astrophysics

This paper is part I of a limited review of the applications of the spectral theory of linear operators in an astrophysical context. The ideal magnetohydrodynamic equations arise in the study of magnetic flux tubes in the solar corona, and in the plasma physics of nuclear containment devices. The system described by these equations is very rich both mathematically and physically, and there are many open problems associated with these models. The underlying mathematical principles are discussed in a qualitative manner in Paper I, and in a more technical manner in subsequent Paper II.