Contraction subgroups and semistable measures on p-adic lie groups

Abstract

Continuous one-parameter semigroups {μ _t}_{t≥ 0} of probability measures on a locally compact group which are semistable with respect to some automorphism t of the group, namely such that t(μ _t) = μ _ct for all t ≥ 0, for a fixed c ε(0, 1), have attracted considerable attention of various researchers in recent years (cf. [3], [5] and other references cited therein). A detailed study of semistable measures on (real) Lie groups is carried out in [5]. In this context it is of interest to study semistable measures on the class of p-adic Lie groups, which is another significant class of locally compact groups.