A Modification of the Lyons-Sullivan Discretization of Positive Harmonic Functions

A modification of the Lyons-Sullivan discretization of positive harmonic functions on a Riemannian manifold M is proposed. This modification, depending on a choice of constants C = {C _n :n = 1,2,..}, allows for constructing measures n_x^C, x ? M\nu_x^\mathbf{C},\ x\in M, supported on a discrete subset Γ of M such that for every positive harmonic function f on M

f(x)=?g ? Gf(g)nCx(g). f(x)=\sum_{\gamma\in\Gamma}f(\gamma)\nu^{\mathbf{C}}_x(\gamma).
Keywords:
本文献已被 SpringerLink 等数据库收录！