In the early 2000's, Littlejohn and Wellman developed a general left-definite
theory for certain self-adjoint operators by fully determining their domains
and spectral properties. The description of these domains do not feature
explicit boundary conditions. We present characterizations of these domains
given by the left-definite theory for all operators which possess a complete
system of orthogonal eigenfunctions, in terms of classical boundary conditions.Comment: 28 page
