Completeness of location families,translated moments,and uniqueness of charges |
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Authors: | L. Mattner |
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Affiliation: | (1) Institut für Mathematische Stochastik, Universität Hamburg, Bundesstrasse 55, W-2000 Hamburg 13, Federal Republic of Germany |
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Abstract: | Summary A sufficient condition for statistical completeness of location families generated by a probability density in euclidean space is given. As an application, completeness of families generated by a symmetric stable law is proved. Our criterion, complementing a classical result of Wiener and recent work of Isenbeck and Rüschendorf, is in terms of regularity of the generating density and zerofreeness of its characteristic function. Its proof rests on a local version of the convolution theorem for Fourier transforms of tempered distributions. A more general version of the criterion is applicable to apparently different problems, as is illustrated by giving a simultaneous proof of a theorem on translated moments by P. Hall and a uniqueness result of M. Riesz in potential theory. |
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Keywords: | 60E10 62F10 44A35 46F10 31B99 |
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