JournalszaaVol. 18, No. 1pp. 13–25

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

  • Dang Dinh Ang

    National University, Hochiminh City, Vietnam
  • Rudolf Gorenflo

    Freie Universität Berlin, Germany
  • Dang Duc Trong

    National University, Hochiminh City, Vietnam
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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.

Cite this article

Dang Dinh Ang, Rudolf Gorenflo, Dang Duc Trong, A Multi-Dimensional Hausdorff Moment Problem: Regularization by Finite Moments. Z. Anal. Anwend. 18 (1999), no. 1, pp. 13–25

DOI 10.4171/ZAA/866