Generalized Tchakaloff's theorem for semi-spectral measures

Lih Chung Wang; Chih-Rung Chen

doi:10.1090/S0002-9939-02-06793-X

Generalized Tchakaloff's theorem for semi-spectral measures

Lih Chung Wang^*, Chih-Rung Chen

^*Corresponding author for this work

Institute of Statistics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We proved the existence of exact quadrature formulae with semipositive definite coefficient matrices for polynomials of prescribed degree in n variables and with respect to a semi-spectral measure. Our proof could be viewed as a direct translation (generalization) of Putinar's result on the existence of quadrature formulae for a positive measure without compact support.

Original language	English
Pages (from-to)	2201-2207
Number of pages	7
Journal	Proceedings of the American Mathematical Society
Volume	131
Issue number	7
DOIs	https://doi.org/10.1090/S0002-9939-02-06793-X
State	Published - 1 Jul 2003

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title = "Generalized Tchakaloff's theorem for semi-spectral measures",

abstract = "We proved the existence of exact quadrature formulae with semipositive definite coefficient matrices for polynomials of prescribed degree in n variables and with respect to a semi-spectral measure. Our proof could be viewed as a direct translation (generalization) of Putinar's result on the existence of quadrature formulae for a positive measure without compact support.",

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AB - We proved the existence of exact quadrature formulae with semipositive definite coefficient matrices for polynomials of prescribed degree in n variables and with respect to a semi-spectral measure. Our proof could be viewed as a direct translation (generalization) of Putinar's result on the existence of quadrature formulae for a positive measure without compact support.

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Generalized Tchakaloff's theorem for semi-spectral measures

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