  Let $Q(z,w)=-\prod_{k=1}^n [(z-a_k)(\bar{w}-\bar{a}_k)-R_k^2]$. 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
$R<\rho_n$, where $z=2\rho_n^2-1$ is the smallest $\ne-1$ zero of the Jacobi
polynomial $\mathcal{P}^{n-2\nu,-1}_\nu(z)$, $\nu=[n/2]$.
