Maximum Entropy In The Finite Stielties And Hamburger Moment Problem

A necessary and sufficient condition for the existence of the maximum entropy (ME) function defined in an infinite or semiinfinite interval, is provided. The conclusions reached show that, except in a few particular cases, the necessary and sufficient conditions for the existence of maximum entropy function are identical to the conditions for the solution of the moment problem when the first M+1 moments are assigned. Even if the conclusions reached are very similar to the Hausdorff case, the specificity of the Hamburger and Stieltjes cases demands a different handling. A sufficient condition for the entropy convergence of the resulting sequence of maximum entropy estimators to the entropy of the recovering function is also provided. PACS numbers: 02.00, 02.30.H, 02.30.M, 02.05 1. Introduction The use of maximum entropy (ME) in the presence of partial information has been a deeply studied technique in the last few decades 1\Gamma2 . The ME principle acts as a criterion to choose among..