The proof of Tchakaloff’s Theorem
Authors:
- Christian BayerCBChristian Bayer
- Josef TeichmannJTJosef Teichmann
- 4 May 2006
- journal article
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 134 (10) , 3035-3040
Abstract
We provide a simple proof of Tchakaloff’s Theorem on the existence of cubature formulas of degree m m for Borel measures with moments up to order m m . The result improves known results for non-compact support, since we do not need conditions on ( m + 1 ) (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.Keywords
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