The Sturm–Liouville group

摘要

In several recent publications Everitt and Markus have developed a theory of ordinary and partial differential boundary value problems, through their novel methods of complex symplectic algebra. For instance, in the case of the regular Sturm–Liouville problem, the corresponding boundary complex symplectic space has four dimensions, and can be used to classify all the self-adjoint boundary conditions by means of two-dimensional Lagrangian subspaces.In this investigation the groups Auto(S), of all symplectic automorphisms, are analyzed for all finite-dimensional complex symplectic spaces S, say of dimension n⩾2; and these are demonstrated to be noncommutative, connected Lie groups of (real) dimension n2. This global topological analysis provides information on continuous families of canonical coordinates in S, and their deformations.