|Title:||Intrinsic topologies on H-contraction groups with applications to semistability|
|Abstract:||Semistable continuous convolution semigroups on Lie groups with non-trivial idempotent are characterized by semistable continuous convolution semigroups with trivial idempotent on a contractible, hence homogeneous Lie group. (Cf., e.g. , , III, theorem 3.5.4.) In fact, this homogeneous group is obtained by a retopologization of the contractible subgroup on which the original semistable laws are concentrated. In  E. Siebert investigated such intrinsic topologies for contractible subgroups of Polish groups, generalizing partially the before mentioned situation of Lie groups. Here we use these ideas to obtain intrinsic topologies for H-contractible subgroups of Polish groups, where H denotes a compact subgroup. This allows, under additional assumptions (which are satisfied in the Lie group case) to obtain similar characterization of semistable laws with non-trivial idempotents.|
|Appears in Collections:||Preprints der Fakultät für Mathematik|
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