The Heyde theorem for locally compact Abelian groups
Copyright policy )The Heyde theorem for locally compact Abelian groups
The author proves a group analogue of the \textit{C. C. Heyde} theorem [Sankhyā, Ser. A 32, 115--118 (1970; Zbl 0209.50702)] where a Gaussian measure is characterized by the symmetry of the conditional distribution of one linear form given another. The paper contains a result of this kind for a locally compact abelian group without subgroups isomorphic to the circle group. The property of measures restored under the Heyde type conditions is to be convolutions of Gaussian measures (in the sense of Parthasarathy) and measures supported in the subgroup generated by all element of order 2.
Gaussian measure, Skitovich-Darmois theorem, Locally compact Abelian group, Probability distributions: general theory, Heyde theorem, Probability measures on groups or semigroups, Fourier transforms, factorization, Analysis
Gaussian measure, Skitovich-Darmois theorem, Locally compact Abelian group, Probability distributions: general theory, Heyde theorem, Probability measures on groups or semigroups, Fourier transforms, factorization, Analysis
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