Irregular sampling in shift invariant spaces of higher dimensions

We consider irregular sampling in shift invariant spaces V of higher dimensions. The problem that we address is: find epsilon so that given perturbations (lambda(k)) satisfying sup vertical bar lambda(k)vertical bar < epsilon, we can reconstruct an arbitrary function f of V as a Riesz basis expansions from its irregular sample values f(k+lambda(k)). A framework for dealing with this problem is outlined and in which one can explicitly calculate sufficient limits epsilon for the reconstruction. We show how it works in two concrete situations.