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