A Bernstein property of measures on groups and symmetric spaces

• Autorzy: Graczyk P. , Loeb J. J.
• Języki publikacji: EN

Abstrakty

EN

In this paper we consider a Bernstein property of probability measures on groups introduced by Neuenschwander. We discuss this property for discrete groups, compact groups, nilpotent groups and some solvable groups. In all these cases we show that a measure having the Bernstein-Neuenschwander property must be concentrated on an Abelian subgroup. We conclude with an application of this result to the Gaussian measures on non-compact symmetric spaces.

Słowa kluczowe

EN

Bernstein property of measures; probability measures on non-commutative groups; Gaussian measures on symmetric spaces

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2000
• Tom: Vol. 20, Fasc. 1
• Strony: 141--149
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Graczyk P.

• Departement de Mathématiques, Université d’Angers, 2 blv. Lavoisier, 49045 Angers, France

autor

Loeb J. J.

• Departement de Mathématiques, Université d’Angers, 2 blv. Lavoisier, 49045 Angers, France

Bibliografia

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• [3] G. M. Feldman, Arithmetic of Probability Distributions and Characterization Problems on Abelian Groups, Math. Monographs, AMS, Vol. 116 (1993).
• [4] G. M. Feldman, On groups for which the Bernstein characterization of the Gaussian distribution is valid, Preprint de l’Université d’Angers, 1999.
• [5] W. Feller, An Introduction to Probability Theory, Vol. 2, Wiley, New York 1966.
• [6] H. Heyerf Probability Measures on Locally Compact Groups, Springer, 1977.
• [7] H. Heyer and Ch. Rail, Gaussche Wahrscheinlichmasse auf Comwinschen Gruppen, Math. Z. 128 (1972), pp. 343-361. '
• [8] D. Neuenschwander, Gauss measures in the sense of Bernstein on the Heisenberg group, Probab. Math. Statist 14 (1993), pp. 253-256.
• [9] D. Neuenschwander, B. Roynette and R, Schott, Characterization of Gauss measures on nilpotent Lie groups and symmetric spaces, C. R. Acad. Sci. Paris 324 (1997), pp. 87-92.
• [10] A. Rukhin, Some statistical and probabilistic problems on groups, Proc. Steklov Inst. Math. III (1970), pp. 59-129.
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