Geometric Characterization of Singular Self-Adjoint Boundary Conditions for Hamiltonian Systems

Abstract

The self-adjoint realizations with separated boundary conditions of rather general differential expressions on an interval [a, b) with a regular and b singular are investiga.ted. The permissible boundary conditions at the singular endpoint are first described in terms of the square integrable solutions of the associated differential equation. Then, for arbitrary (equal) deficiency indices, they are characterized using the M-functions lying on the boundary of the limiting object of the Weyl circles, thus generalizing a well-known result for Sturm-Liouville operators.

Keywords:

• ordinary differential operators
• singular self-adjoint boundary conditions
• Wehl theory