Absorbent, parabolic, elliptic and quasielliptic balayages in potential theory; relationships with the Green function (Q1347112)

The authors study absorbent, parabolic, elliptic and quasielliptic sets with respect to a standard \(H\)-cone of functions. Note that a standard \(H\)-cone of functions is always isomorphic to the cone of all excessive functions with respect to a submarkovian resolvent of kernels with reference measure on a measurable space. Using Green's functions the authors are characterizing absorbent, parabolic, elliptic and quasielliptic sets. They also verify that parabolic, elliptic and quasielliptic sets are the same with respect to a standard \(H\)-cone as with respect to its dual.