A new characterization of singular self-adjoint boundary conditions for Sturm-Liouvillc problems is given. These arc an exact parallel of the regular case. They arc given explicitly in terms of principal and non-principal solutions. The special nature of the Friedrichs extension is clearly apparent and highlighted. Inequalities among the eigenvalues of different boundary conditions, separated and coupled, are obtained. Most of all we want to stress the method of proof. It is based on a very elementary transformation which transforms any singular non-oscillatory limit-circle endpoint into a regular one.

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