Automorphisms on a Lie group contracting modulo a compact subgroup and applications to semistable convolution semigroups |
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Authors: | W Hazod E Siebert |
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Institution: | (1) Fachbereich Mathematik der Universität, 4600 Dortmund 50, West Germany;(2) Mathematisches Institut der Universität, 7400 Tübingen 1, West Germany |
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Abstract: | Let (
t
)
t0 be a -semistable convolution semigroup of probability measures on a Lie groupG whose idempotent
0 is the Haar measure on some compact subgroupK. Then all the measures
1
are supported by theK-contraction groupC
K() of the topological automorphism ofG. We prove here the structure theoremC
K()=C()K, whereC() is the contraction group of . Then it turns out that it is sufficient to study semistable convolution semigroups on simply connected nilpotent Lie groups that have Lie algebras with a positive graduation. |
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Keywords: | Automorphisms of a Lie group K-contraction group Borel cross section semistable convolution semigroup |
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