A duality proof of Tchakaloff's theorem

Raul E Curto; Lawrence A Fialkow

doi:10.1016/s0022-247x(02)00034-3

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A duality proof of Tchakaloff's theorem

Raul E Curto and Lawrence A Fialkow

Journal of Mathematical Analysis and Applications, Vol.269(2), pp.519-532

07/06/2002

DOI: 10.1016/s0022-247x(02)00034-3

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Abstract

Tchakaloff's Theorem establishes the existence of a quadrature rule of prescribed degree relative to a positive, compactly supported measure that is absolutely continuous with respect to Lebesgue measure on $\mathbb{R}^{d}$. Subsequent extensions were obtained by Mysovskikh and by Putinar. We provide new proofs and partial extensions of these results, based on duality techniques utilized by Stochel. We also obtain new uniqueness criteria in the Truncated Complex Moment Problem.

Analysis

Mathematics - Functional Analysis

Applied Mathematics

Details

Title: Subtitle: A duality proof of Tchakaloff's theorem
Creators: Raul E Curto
Lawrence A Fialkow
Resource Type: Journal article
Publication Details: Journal of Mathematical Analysis and Applications, Vol.269(2), pp.519-532
DOI: 10.1016/s0022-247x(02)00034-3
ISSN: 0022-247X
Publisher: Elsevier BV
Language: English
Date published: 07/06/2002
Academic Unit: Mathematics
Record Identifier: 9983985953802771

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