The proof of Tchakaloff's theorem

被引：75

作者：

Bayer, Christian ^{[1
]}

Teichmann, Josef ^{[1
]}

机构：

[1] Vienna Tech Univ, A-1040 Vienna, Austria

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2006年 / 134卷 / 10期

关键词：

quadrature; cubature; truncated moment problem; Tchakaloff's theorem;

D O I：

10.1090/S0002-9939-06-08249-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We provide a simple proof of Tchakalo.'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 Tchakalo.'s Theorem to a well-known statement going back to F. Riesz.

引用

页码：3035 / 3040

页数：6

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