Extremal properties of strong quadrature weights and maximal mass results for truncated strong moment problems

A bisequence of complex numbers {μn}−∞∞ determines a strong moment functional L satisfying L[xn] = μn. 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 {wni,xni} exist such that μk = ∑i=innsnikwni. This paper is concerned with establishing certain extremal properties of the weights wni and using these properties to obtain maximal mass results satisfied by distributions ψ(x) representing L when only a finite bisequence of moments {μk}k=−nn−1 is given.