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Do non-strictly stable laws on positively graduated simply connected nilpotent Lie groups lie in their own domain of normal attraction?

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Domain of normal attraction, stable semigroup, simply connected nilpotent Lie group, Heisenberg group, group of type H.

Geometric stable and semistable distributions on (Z+)^d

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Semigroup, geometric infinite divisibility, branching processes, mixture representation, domain of geometric attraction

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