The multidimensional truncated moment problem: Carathéodory numbers from Hilbert functions
The multidimensional truncated moment problem: Carathéodory numbers from Hilbert functions
In this paper we improve the bounds for the Carath\'eodory number, especially on algebraic varieties and with small gaps (not all monomials are present). We provide explicit lower and upper bounds on algebraic varieties, $\mathbb{R}^n$, and $[0,1]^n$. We also treat moment problems with small gaps. We find that for every …