Removability of polar sets for energy finite harmonic functions on harmonic spaces with adjoint structure (Q2640737)

In classical potential theory it is known that polar sets are removable for Dirichlet-finite harmonic functions. The author proves, in the context of harmonic spaces with adjoint structure, that polar sets are removable for harmonic functions with finite energy. Since the energy and the Dirichlet integral coincide in the case where the constant functions are harmonic, the classical result follows as a special case and it also follows that heat polar sets are removable for Dirichlet-finite solutions of the heat equation.