Every non-negative superharmonic function u on Ω decomposes as Newtonian-potential of Riesz-measure + harmonic remainder: u = ∫G(x,y) dμ(y) + h. Generalises Liouville theorem. Foundation for Martin boundary + boundary representations.
Every non-negative superharmonic function u on Ω decomposes as Newtonian-potential of Riesz-measure + harmonic remainder: u = ∫G(x,y) dμ(y) + h. Generalises Liouville theorem. Foundation for Martin boundary + boundary representations.