Abstract
A bisequence of complex numbers { μ n } −∞ ∞ determines a strong moment functional L satisfying L[ x n ] = μ n . If L is positive-definite on a bounded interval ( a, b) ⊂ R{0}, then L has an integral representation L , n=0, ±1, ±2,…, and quadrature rules { w ni , x ni } exist such that μ k = ∑ i= i n n s ni k w ni . This paper is concerned with establishing certain extremal properties of the weights w ni and using these properties to obtain maximal mass results satisfied by distributions ψ( x) representing L when only a finite bisequence of moments { μ k } k=− n n−1 is given.
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