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Semistable convolution semigroups and the topology of contraction groups. (English) Zbl 0699.22002

Probability measures on groups IX, Proc. 9th Conf., Oberwolfach/FRG 1988, Lect. Notes Math. 1379, 325-343 (1989).
[For the entire collection see Zbl 0667.00022.]
Let G be a topological group and let \(\tau\in Aut(G)\). The contraction group \(c(\tau)\) of \(\tau\) is defined by \(c(\tau)=\{x\in G\); \(\lim_{n\geq 1}\tau^ n(x)=e\}\). The author deals with the problem of retopologizing \(c(\tau)\) to yield a topological group \(\tilde c(\tau)\) that has the same properties as G and that supports the \(\tau\)-semistable convolution semigroups of G. He proves that this can be done in the category of complete and metrizable groups but this is not possible in the category of locally compact groups. He also considers several examples.
Reviewer: P.Das

MSC:

22A05 Structure of general topological groups
43A55 Summability methods on groups, semigroups, etc.
60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
43A05 Measures on groups and semigroups, etc.

Citations:

Zbl 0667.00022