## 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.## References

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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