Optimization approaches to quadrature: new characterizations of Gaussian quadrature on the line and quadrature with few nodes on plane algebraic curves, on the plane and in higher dimensions

Cordian Riener, Markus Schweighofer

Let $d$ and $k$ be positive integers. Let $\mu$ be a positive Borel measure on ${\mathbb{R}}^2$ possessing finite moments up to degree $2d-1$. If the support of $\mu$ is contained in an…