The Hausdorff entropic moment problem

(O)ur aim in this paper is twofold. First, to find the necessary and suffic ient conditions to be satisfied by a given sequence of real numbers {omega (n)}(n=0)(infinity) to represent the "entropic moments" integral ([0,a])[rh o (x)](n)dx of an unknown non-negative, decreasing and differentiable (a.e. ) density function rho (x) with a finite interval support. These moments ar e called entropic moments because they are closely connected with various i nformation entropies (Renyi, Tsallis, ...). Second, we outline an efficient method for the reconstruction of the density function from the knowledge o f its first N entropic moments. (C) 2001 American Institute of Physics.