Abstract
Sturm-Liouville (S-L) boundary value problems on any finite number of intervals are studied in the setting of the direct sum of the $L_\omega ^2$-spaces of functions defined on each of the separate intervals. The interplay between these $L_\omega ^2$-spaces is of critical importance. This study is partly motivated by the occurrence of (S-L) problems with coefficients that have a singularity in the interior of the basic interval. In the one interval case, the singular self-adjoint boundary conditions are characterized in terms of certain Wronskians involving y and two linearly independent solutions of M[y] = 0 by Krall and Zettl in [11].