IRREGULAR SAMPLING IN SHIFT INVARIANT SPACES OF HIGHER DIMENSIONS

Abstract

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