Characterization of symmetric operators and their Friedrichs extension for singular Sturm-Liouville problems (Q831482)

In this work it is considered the general singular Sturm-Liouville equation. First the principal and non-principal solutions for general singular Sturm-Liouville equation are discussed. These concepts will be used for construction of the boundary conditions of the symmetric operators for limit-circle second order symmetric differential equations in the next sections. The Friedrichs extension of each of these symmetric operators which is bounded below is found and some examples of Friedrichs conditions for some of these symmetric operators are given. The obtained results are new and are of scientific interest.