2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/138860Let $Q(z,w)=-\prod_{k=1}^n [(z-a_k)(\bar{w}-\bar{a}_k)-R_k^2]$. M. Putinar and B. Gustafsson proved recently that the matrix $Q(a_i,a_j)$, $1\leq i,j\leq n$, is positive definite if disks $|z-a_i|<R_i$ form a disjoint collection. We extend this result on symmetric collections of discs with overlapping. More precisely, we show that in the case when the nodes $a_j$ are situated at the vertices of a regular $n$-gon inscribed in the unit circle and $\forall i: R_i\equiv R$, the matrix $Q(a_i,a_j)$ is positive definite if and only if $R<ρ_n$, where $z=2ρ_n^2-1$ is the smallest $\ne-1$ zero of the Jacobi polynomial $\mathcal{P}^{n-2ν,-1}_ν(z)$, $ν=[n/2]$.24 pagesComplex VariablesMetric Geometry30E05; 15A48; 33C10; 26C10text