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Completeness of location families, translated moments, and uniqueness of charges
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  • Published: June 1992

Completeness of location families, translated moments, and uniqueness of charges

  • L. Mattner1 

Probability Theory and Related Fields volume 92, pages 137–149 (1992)Cite this article

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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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Authors and Affiliations

  1. Institut für Mathematische Stochastik, Universität Hamburg, Bundesstrasse 55, W-2000, Hamburg 13, Federal Republic of Germany

    L. Mattner

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  1. L. Mattner
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Mattner, L. Completeness of location families, translated moments, and uniqueness of charges. Probab. Th. Rel. Fields 92, 137–149 (1992). https://doi.org/10.1007/BF01194918

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  • Received: 15 March 1991

  • Issue Date: June 1992

  • DOI: https://doi.org/10.1007/BF01194918

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Mathematics Subject Classification (1985)

  • 60E10
  • 62F10
  • 44A35
  • 46F10
  • 31B99
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