M. Frontini, A. Tagliani Dipartimento di Matematica, Politecnico di Milano, Piazza L. da Vinci 32-20133 MilanoItaly

The finite moment problem in the framework of maximum entropy approach is numerically investigated to recover a positive density function. Numerical experiments suggest that a few moments can be effectively used as the moment space geometry. If an high machine precision is adopted, an estimate of the information content of a recovered function can be obtained. 1. Introduction The moment problem by Maximum Entropy (M.E.) approach has been widely studied [1]. Only recently the existence problem has been completely solved [2,3]. The recent theoretical results on the existence and unicity of M.E. solution have put a new light on the ill-posedness and on the difficulties of the numerical solvability of the finite moment problem when a positive solution is required. Some results concerning the convergence problem have been provided in [3,4]. A lot of problems lead to the generalized moment problem, consisting in the recovery of a positive function f(x), defined in a domain R, knowing only th..