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Limits of commutative triangular systems on real and p-adic groups

Published online by Cambridge University Press:  24 October 2008

Riddhi Shah
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road. Bombay 400 005, India

Extract

A fundamental theorem of Khinchin says that every limit of an infinitesimal triangular system of probability measures on R is infinitely divisible. This was generalized to all divisible locally compact second countable abelian groups by Parthasarathy et al. (cf. [PRV]). Recently, Ruzsa eliminated the second countability condition and also proved the theorem for all Banach spaces (cf. [R2]). A similar theorem was also proved by Gangolli for certain symmetric spaces (cf. [G]). A result of Carnal shows that infinite divisibility of limits holds for commutative infinitesimal triangular systems on compact groups (cf. [C]). The same was recently proved by Neuenschwander for simply connected step-2 nilpotent Lie groups, provided the system is symmetric or supported on a discrete subgroup (cf. [N]).

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1996

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