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- W2070040143 abstract "A notion of admissible probability measures μ on a locally compact Abelian group (LCA - group) G with connected dual group Ĝ = ℝd × 𝕋n is defined. To such a measure μ, a closed semigroup Λ(μ) ⊆ (0, ∞) can be associated, such that, for t ∈ Λ(μ), the Fourier transform to the power t, (μˆ)t, is a characteristic function. We prove that the existence of roots for non admissible probability measures underlies some restrictions, which do not hold in the admissible case. As we show for the example ℤ2, in the case of LCA - groups with non connected dual group, there is no canonical definition of the set Λ(μ)." @default.
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- W2070040143 date "2000-05-01" @default.
- W2070040143 modified "2023-09-26" @default.
- W2070040143 title "Partly Divisible Probability Measures on Locally Compact Abelian Groups" @default.
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- W2070040143 doi "https://doi.org/10.1002/(sici)1522-2616(200005)213:1<5::aid-mana5>3.0.co;2-q" @default.
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