Harmonic functions on hypergroups (Q639513)

This paper is devoted to harmonic functions on certain classes of hypergroups. In particular, for hypergroups, which are nilpotent in the sense of the authors. The authors present Liouville theorems for bounded harmonic functions as well as a representation of positive harmonic functions as integrals of so-called exponential functions. Furthermore, it is shown that these hypergroups always admit a Haar measure. Moreover, a Harnack inequality and a Liouville theorem for compact hypergroups are given. Finally, double coset hypergroups are also considered. The reviewer is not sure whether the definition of nilpotence of the authors is the optimal one as the restriction to supernormal subhypergroups seems to be quite restrictive.