Singularity of cardinal interpolation with shifted box splines (Q1260632)

Let \(M_{n,n,n}\) \((n=1,2,\dots)\) denote the bivariate centered box spline with directions \((1,0)\), \((0,1)\), and \((1,1)\), each repeated \(n\) times. Further, let \(M_{n,\omega}:= M_{n,n,n}(\cdot+\omega)\) denote the shifted box spline. The main result of this paper states that the cardinal interpolation operator corresponding to \(M_{n,\omega}\) is invertible if and only if \(\omega\in(-1/2,1/2)^ 2\cap\{(s,t): | s- t|< 1/2\}\).