The restricted mean value property for sublaplacians (Q1364564)

The author proves the restricted mean value property for a special class of degenerate elliptic operators \(L\). On solid ``balls'' defined in terms of the Green function \(G\) a canonical representing measure for \(L\)-harmonic functions is given by the density \({1 \over \zeta} LG^{-\zeta} (\cdot,x)\) with respect to Lebesgue measure. Assuming the hypotheses needed for the case \(L= \Delta\) and adding some mild conditions on \(G\) he proves his assertion using Schrödinger equation arguments.