Zeitschrift für Analysis und ihre Anwendungen Vol. 18, No. 1, pp. 1325 (1999) 

A MultiDimensional Hausdorff Moment Problem: Regularization by Finite MomentsD. D. Ang, R. Gorenflo and D. D. TrongD. D. Ang: Nat. Univ., Dept. Math., 227 Nguyen Van Cu, Q5, Hochiminh City, VietnamR. Gorenflo: Freie Universität Berlin, FB Math. und Inf., Arnimallee 26, D14195 Berlin D. D. Trong: Nat. Univ., Dept. Math., 227 Nguyen Van Cu, Q5, Hochiminh City, Vietnam Abstract: We consider the multidimensional 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 powerproducts 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: illposed problems, Hausdorff moment problem, polynomial approximation Classification (MSC2000): 65R30, 41A10 Full text of the article:
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