Friedrichs extension

Summary

The Friedrichs extension is a canonical self-adjoint extension of a densely defined symmetric operator that is bounded below. It is built from the quadratic form of the operator, by completing the domain in the form norm. It has the same lower bound as the original operator. It is the standard way to turn a formal differential operator such as $-\Delta + V$ with $V \ge 0$ into a self-adjoint operator.