On the application of maximum entropy to the moments problem

The maximum-entropy approach to the solution of classical inverse problem of moments, in which one seeks to reconstruct a function p(x) [where x∈(0,+∞)] from the values of a finite set N+1 of its moments, is studied. It is shown that for N≥4 such a function always exists, while for N=2 and N=3 the acceptable values of the moments are singled out analytically. The paper extends to the general case where the results were previously bounded to the case N=2.