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Solution of the Truncated Parabolic Moment Problem

Authors:	Raúl?E.?Curto mailto:rcurto@math.uiowa.edu" title=" rcurto@math.uiowa.edu" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,Lawrence?A.?Fialkow

Affiliation:	(1) Department of Mathematics, The University of Iowa, Iowa City, IA 52242-1419, USA;(2) Department of Computer Science, State University of New York, New Paltz, NY 12561, USA

Abstract:	Given real numbers $beta equiv beta ^{(2n)} = { beta _{ij} } _{i,j geq 0,i + j leq 2n} ,$ with ₀₀ >0 , the truncated parabolic moment problem for entails finding necessary and sufficient conditions for the existence of a positive Borel measure , supported in the parabola p(x, y) = 0, such that $beta _{ij} = int {y^i x^j } dmu quad (0, leq ,i, + ,j, leq ,2n)$ We prove that admits a representing measure (as above) if and only if the associated moment matrix is positive semidefinite, recursively generated and has a column relation p(X, Y) = 0, and the algebraic variety () associated to satisfies card In this case, admits a rank -atomic (minimal) representing measure.Submitted: August 25, 2003

Keywords:	Primary 47A57 44A60 42A70 30A05 Secondary 15A57 15-04 47N40 47A20
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