Moments of non-negative mass

Source abstract

Abstract A sequence {ak(t)} (k = 1 ,2 ,...), of real-valued functions of a real variable t is given, defined in an interval I (possibly unbounded) which may be closed, open, or half open. The corresponding moment problem is to determine the set ℭ of all real sequences {ck.} for which the equations ∫ ak(t) dµ(t) = ck have non-decreasing functions µ(t) as solutions. The associated ‘reduced’ moment problem (1≤k≤n) is completely answered without any restrictions on the ak(t). The full problem is solved under suitable restrictions on the ak(t), and the ‘geometrical’ theory developed in this paper contains and generalizes the classical theory of moment problems. In particular, it permits to treat, as a special case, systems of linear equations in an infinity of non-negative unknowns.