MAXIMUM-ENTROPY IN THE HAMBURGER MOMENTS PROBLEM

The maximum-entropy approach to the solution of the Hamburger inverse problem of moments, in which one seeks to recover a positive density function p(x) [where x epsilon(-infinity, +infinity)] from the values of a finite N + 1 of its moments, is considered. The obtained results show that unexpected upper bounds for the moments do not exist in the general Hamburger finite moment problem, unlike in the symmetric case previously considered. Some physical examples, illustrating the use of partial information to determine the approximate function, are presented.