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The proof of Tchakaloff's Theorem
Author(s):
Christian
Bayer;
Josef
Teichmann
Journal:
Proc. Amer. Math. Soc.
134
(2006),
3035-3040.
MSC (2000):
Primary 65D32, 52A21
Posted:
May 4, 2006
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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:
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
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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