CONTRACTION SEMIGROUPS ON HYPERGROUP ALGEBRAS

In this paper we develop potential theory on hypergroups and study contrac- tion semigroups on hypergroups, we state and prove a necessary and sufficient condition that the domain of zero-resolvent or the domain of potential operator of {Pt}t>0 is dense in L 2 (K). 1. Introduction and Notation Let K be a commutative locally compact hypergroup. We denote by M (K) the space of all regular complex-valued Borel measures on K ,b yM + (K) the subset of positive measures in M (K), and by δx the Dirac measure at the point x. The closure of any A ⊆ K is denoted by A c .