Moments of non-negative mass
A sequence { a k ( 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 { c k .} for which the equations ∫ a k ( t ) d µ ( t ) = c k have non-decreasing functions µ ( t ) as solutions. The associated ‘reduced’ moment problem (1≤ k ≤ n ) is completely answered without any restrictions on the a k ( t ). The full problem is solved under suitable restrictions on the a k ( 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.