Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Generalized Tchakaloff's theorem for semi-spectral measures

Author(s): Lih-Chung Wang; Chih-Rung Chen
Journal: Proc. Amer. Math. Soc. 131 (2003), 2201-2207.
MSC (2000): Primary 65D32, 44A60
Posted: 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 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.

References:

1.: R. E. Curto and L. Fialkow, Flat extensions of positive moment matrices: relations in analytic or conjugate terms, Oper. Theory Adv. Appl., 104, 1998. MR 99i:47026
2.: S. Karlin and W. J. Studden, Tchebycheff Systems: With Applications in Analysis and Statistics, Pure and Applied Mathematics, Vol. XV, Interscience, 1966. MR 34:4757
3.: M. Putinar, A note on Tchakaloff's theorem, Proc. Amer. Math. Soc. 125 (1997), no. 8, 2409-2414. MR 97j:65045
4.: A. H. Stroud, Approximate Calculation of Multiple Integrals, Prentice-Hall, Englewood Cliffs, New Jersey, 1971. MR 48:5348
5.: V. Tchakaloff, Formules de cubature mécanique à coefficients non négatifs, Bull. Sci. Math. 81 (1957), 123-134. MR 20:1145

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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: 10.1090/S0002-9939-02-06793-X
PII: S 0002-9939(02)06793-X
Received by editor(s): March 1, 2001
Received by editor(s) in revised form: February 12, 2002
Posted: 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
Copyright of article: Copyright 2002, American Mathematical Society

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