Harmonic space

Summary

A harmonic space is a locally compact space with a sheaf of continuous functions, called harmonic, that obey axioms modelled on classical harmonic functions. The axioms ask that the Dirichlet problem be uniquely solvable on a base of small open sets. They also ask that suitable increasing limits of harmonic functions be harmonic. Harmonic spaces are the main setting of axiomatic potential theory. Euclidean space with the Laplace equation is a harmonic space, and so is space-time with the heat equation.