Contraction subgroups and semistable measures on p-adic lie groups

Continuous one-parameter semigroups {&#956; <SUB>t</SUB>}<SUB>t&#8805; 0</SUB> of probability measures on a locally compact group which are semistable with respect to some automorphism t of the group, namely such that t(&#956; <SUB>t</SUB>) = &#956; <SUB>ct</SUB> for all t &#8805; 0, for a fixed c &#949;(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