= Friedrichs extension
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A densely defined semibounded <symmetric operator> on a <Hilbert space> has a canonical semibounded extension that is a <self-adjoint operator> obtained by closing its <quadratic form>. After shifting the lower bound to zero, complete the initial form domain in the norm $(\|u\|^2+q[u])^{1/2}$; the associated closed form determines the Friedrichs extension. For the <positive Laplace-Beltrami operator> on a polygonal surface, this specifies the finite-energy realization at corners. Different choices of the initial form domain impose <Dirichlet boundary conditions>, <Neumann boundary conditions>, or mixed <boundary conditions>; the extension does not choose the boundary condition independently of that domain.
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