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The proof of Tchakaloff's Theorem
Authors:
Christian Bayer and Josef Teichmann
Journal:
Proc. Amer. Math. Soc. 134 (2006), 3035-3040
MSC (2000):
Primary 65D32, 52A21
Posted:
May 4, 2006
MathSciNet review:
2231629
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Abstract: We provide a simple proof of Tchakaloff's Theorem on the existence of cubature formulas of degree  for Borel measures with moments up to order  . The result improves known results for non-compact support, since we do not need conditions on  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
Email:
jteichma@fam.tuwien.ac.at
DOI:
http://dx.doi.org/10.1090/S0002-9939-06-08249-9
PII:
S 0002-9939(06)08249-9
Keywords:
Quadrature,
cubature,
truncated moment problem,
Tchakaloff's Theorem
Received by editor(s):
March 7, 2005
Received by editor(s) in revised form:
May 3, 2005
Posted:
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\textquotedblright 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
Article copyright:
© Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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