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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The proof of Tchakaloff’s Theorem
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by Christian Bayer and Josef Teichmann PDF
Proc. Amer. Math. Soc. 134 (2006), 3035-3040 Request permission

Abstract:

We provide a simple proof of Tchakaloff’s Theorem on the existence of cubature formulas of degree $m$ for Borel measures with moments up to order $m$. The result improves known results for non-compact support, since we do not need conditions on $(m+1)$st moments. In fact, we reduce the classical assertion of Tchakaloff’s Theorem to a well-known statement going back to F. Riesz.
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Additional Information
  • Christian Bayer
  • Affiliation: Technical University of Vienna, e105, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria
  • Email: cbayer@fam.tuwien.ac.at
  • Josef Teichmann
  • Affiliation: Technical University of Vienna, e105, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria
  • MR Author ID: 654648
  • Email: jteichma@fam.tuwien.ac.at
  • Received by editor(s): March 7, 2005
  • Received by editor(s) in revised form: May 3, 2005
  • Published electronically: May 4, 2006
  • Additional Notes: The authors are grateful to Professor Peter Gruber for mentioning the word “Stützebene” in the right moment. The first author acknowledges the support from FWF-Wissenschaftskolleg “Differential Equations” W 800-N05. The second author acknowledges the support from the RTN network HPRN-CT-2002-00281 and from the FWF grant Z-36.
  • Communicated by: Andreas Seeger
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 3035-3040
  • MSC (2000): Primary 65D32, 52A21
  • DOI: https://doi.org/10.1090/S0002-9939-06-08249-9
  • MathSciNet review: 2231629