Convergence of cardinal series

The result of this paper is a generalization of our characterization of the limits of multivariate cardinal splines. Let denote the -fold convolution of a compactly supported function <!-- MATH $M \in {L_2}({{\mathbf{R}}^d})$ --> and denote by <!-- MATH \begin{displaymath} {S_n}: = \left\{ {\sum\limits_{j \in {{\mathbf{Z}}^d}} {c(j){M_n}( \cdot - j):c \in {l_2}({{\mathbf{Z}}^d})} } \right\} \end{displaymath} -->