Multiple decomposability of probabilities on contractible locally compact groups
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Date
2011-02-16
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Abstract
Operator decomposable probabilities on vector spaces
– generalizing (semi-)stable and self-decomposable laws – are well
known. More specific concepts, multiple operator decomposable
laws, generalizing the nested Urbanik classes in the case of selfdecomposability,
were investigated in fundamental papers by Maejima
et al. [16], [17] resp. by Maejima and R. Shah [18] for real
resp. p-adic vector spaces. For locally compact groups, decomposability
properties were studied by R. Shah [27], Raja [23], see
also [6]. Here we are concerned with multiple decomposability on
locally compact groups and generalize – as far as possible – the
results in [16], [18]. In fact, as it turned out that contraction properties
play an essential role, hence throughout we concentrate on
contractible locally compact groups.