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Zeitschrift für Analysis und ihre Anwendungen


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Volume 18, Issue 1, 1999, pp. 13–25
DOI: 10.4171/ZAA/866

Published online: 1999-03-31

A Multi-Dimensional Hausdorff Moment Problem: Regularization by Finite Moments

Dang Dinh Ang[1], Rudolf Gorenflo[2] and Dang Duc Trong[3]

(1) National University, Hochiminh City, Vietnam
(2) Freie Universität Berlin, Germany
(3) National University, Hochiminh City, Vietnam

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

Ang Dang Dinh, Gorenflo Rudolf, Trong Dang Duc: A Multi-Dimensional Hausdorff Moment Problem: Regularization by Finite Moments. Z. Anal. Anwend. 18 (1999), 13-25. doi: 10.4171/ZAA/866