Gnew = ResponseFunction.PlaceOnMesh(Gold, EnergyTable) takes a response function Gold and a list doubles, EnergyTable. The poles of Gnew are given by the EnergyTable. All poles of Gold are copied to Gnew whereby the residue of a pole at Eold is shared between the poles in Gnew with nearest energy that is below and above Eold. Gnew conserves the zeroth and first moment of Gold.