APPROXIMATE SOLUTIONS FOR A FINITE MOMENT PROBLEM G. INGLESE (1) ABSTRACT - We study the problem of recovering a function whose first moments are known, possibly contaminated by noise. We evaluate accuracy and stability of a step function approximation using additional information about the L 2 norm of the derivative; finally we show the results of some numerical experiments. 1. A Finite Dimensional Moment Problem Let u be a real continuously differentiable function on (0,1) and let e, E, #j (j = 1,...,n) be real numbers such that: 1 li/ j=l o ~ (ii) ~ ~j2 > 82, j=l 1 (iii) f u'(x)2dx E 2. 0 Our problem, closely related to the Hausdorff Moment Problem(HMP) consists in finding an approximation of u with functions chosen in a finite dimensional subspace Xn of L2(0,1) and in estimating accuracy and stability of such an appro- ximation. A broad introduction to HMP, with a rigorous argument proving the ill-posedness, can be found in [9]. We consider Xn as the set of the step functions on (0,1) of the form (1) v(x) = k=l alO~Ik(X) ak E IR, Received 15 September 1988. (1) C.N.R. - Istituto di Analisi Globale e Applicazioni, Via S. Marta 13/A, 50139 Firenze.