A duality proof of Tchakaloff's theorem

2002/07/06 by Raul E. Curto, Lawrence A. Fialkow · 1 citation
Mathematics · #math.FA #msc:47A57 #msc:46A20 #msc:65D32 #msc:44A60

paper · pdf

published as J. Math. Anal. Appl. 269(2002), 519-532 · 16 pages

arxiv created 2002/07/06 · arxiv updated 2009/11/30

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 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.

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