Details

Autor(en) / Beteiligte

• Albeverio, Sergio
• Gottschalk, Hanno
• Wu, Jiang-Lun

Titel

Partly Divisible Probability Measures on Locally Compact Abelian Groups

Ist Teil von

• Mathematische Nachrichten, 2000-05, Vol.213 (1), p.5-15

Ort / Verlag

Berlin: WILEY-VCH Verlag Berlin GmbH

Erscheinungsjahr

2000

Quelle

Wiley Online Library Journals Frontfile Complete

Beschreibungen/Notizen

• 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).