Contraction subgroups and semistable measures on p-adic lie groups

Dani, S. G. ; Shah, Riddhi (1991) Contraction subgroups and semistable measures on p-adic lie groups Mathematical Proceedings of the Cambridge Philosophical Society, 110 (2). pp. 299-306. ISSN 0305-0041

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Related URL: http://dx.doi.org/10.1017/S0305004100070377

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.

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