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 is-an-element-of(0, + infinity)] from the values of a finite set N + 1 of its moments, is studied. It is shown that for N greater-than-or-equal-to 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.