The Friedrichs extension of a second order singular elliptic operator is considered on a weighted £*(tø) space. The region tø is not necessarily bounded. Necessary conditions and sufficient conditions on the coefficients that will insure a discrete spectrum are given with a certain degree of sharpness achieved. The boundary conditions include the Dirichlet, Neumann, and mixed Dirichlet-Neumann boundary value problems. © 1982 American Mathematical Society.