arXiv subjects
Publications and source records attributed to H. N. Friedel.
There is a natural isomorphism from image to complement of nullspace, for a bounded linear map from a real Banach space onto a closed subspace of a real Hilbert space. This generalizes Riesz representation (self-duality of Hilbert space). The isomorphism helps solve the pressure equation of fluid dynamics.
A densely-defined symmetric linear map from/to a real Hilbert space extends to a self-adjoint map. Extension is expressed via Riesz representation. For a case including Friedrichs extension of a strongly monotone map, self-adjoint extension is unique, and equals closure of the given map.
A standard Hilbert-space proof of Dirichlet's principle is simplified, using an observation that a certain form of min-problem has unique solution, at a specified point. This solves Dirichlet's problem, after it is recast in the required form (using the Poincare/Friedrichs bound and Riesz representation). The solution's dependence on data is linear and continuous; and the solution is invariant under certain changes of data, away from the border of the region where Dirichlet's problem is given. If that region is regular enough for functions on it to have border-traces, then the problem can be stated and solved in terms of border-data.