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Proceedings of the American Mathematical Society

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Generalized Tchakaloff's theorem for semi-spectral measures


Authors: Lih-Chung Wang and Chih-Rung Chen
Journal: Proc. Amer. Math. Soc. 131 (2003), 2201-2207
MSC (2000): Primary 65D32, 44A60
Published electronically: November 6, 2002
MathSciNet review: 1963768
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Abstract: We proved the existence of exact quadrature formulae with semi-positive 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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Additional Information

Lih-Chung Wang
Affiliation: Department of Applied Mathematics, National Donghwa University, Shoufeng, Hualien 974, Taiwan
Email: lcwang@mail.ndhu.edu.tw

Chih-Rung Chen
Affiliation: Institute of Statistics, National Chiao Tung University, Hsinchu 300, Taiwan
Email: cchen@stat.nctu.edu.tw

DOI: https://doi.org/10.1090/S0002-9939-02-06793-X
Received by editor(s): March 1, 2001
Received by editor(s) in revised form: February 12, 2002
Published electronically: November 6, 2002
Additional Notes: This paper was partially supported by the National Science Council (NSC-87-2119-M-259-004)
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2002 American Mathematical Society