Zeitschrift für Analysis und ihre Anwendungen
Vol. 18, No. 1, pp. 13-25 (1999)
A Multi-Dimensional Hausdorff Moment Problem: Regularization by Finite Moments
D. D. Ang, R. Gorenflo and D. D. TrongD. D. Ang: Nat. Univ., Dept. Math., 227 Nguyen Van Cu, Q5, Hochiminh City, Vietnam
R. Gorenflo: Freie Universität Berlin, FB Math. und Inf., Arnimallee 2--6, D-14195 Berlin
D. D. Trong: Nat. Univ., Dept. Math., 227 Nguyen Van Cu, Q5, Hochiminh City, Vietnam
Abstract: We consider the multi-dimensional Hausdorff moment problem over the unit cube: to reconstruct an unknown function from the (inaccurately) given values of the integrals of the unknown function multiplied by all power-products of the independent variables. We describe a regularization scheme using orthogonalization by the tensor product of (shifted) Legendre polynomials and approximation of the unknown function by a finite sum, the dimension of the space of approximation playing the role of the regularization parameter. For the case of square integrability of the unknown function we present an estimate of the regularization error that implies convergence if the data error tends to zero.
Keywords: ill-posed problems, Hausdorff moment problem, polynomial approximation
Classification (MSC2000): 65R30, 41A10
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Electronic fulltext finalized on: 25 Apr 2000. This page was last modified: 9 Nov 2001.