Extremal properties of strong quadrature weights and maximal mass results for truncated strong moment problems (Q1360167)

The study of strong moment functionals connected with doubly infinite sequences of complex numbers \(\{\mu_n\}_{-\infty}^\infty\) has received quite a lot of attention lately. It is known that, if the moment functional \(\mathcal L\) is positive definite on a bounded interval \([a,b]\subset\mathbb{R}\setminus\{0\}\), then \(\mathcal L\) has an integral representation and, moreover, quadrature rules \(\{w_{ni},x_{ni}\}\) exist with \[ \mu_k=\sum_{i=1}^{\nu_n} x_{ni}^kw_{ni}. \] Here the \(x_{ni} (1\leq i\leq\nu_n)\) are the real distinct zeros of the orthogonal Laurent polynomial sequence (actually \textit{rational functions}) connected with \(\mathcal L\). After establishing general extremal properties of the weights \(w_{ni}\), the authors turn to the case that only a finite part of the moment sequence is given: \(\{\mu_k\}_{k=-n}^{n-1}\). They then give maximal mass results for distributions \(\psi(x)\) that represent \(\mathcal L\) in this truncated case.