Reconstruction of Multiply Generated Splines from Local Average Samples

Abstract

We analyze the following average sampling problem: Let h be a nonnegative measurable function supported in − 1 2 , 1 2 . Given a sequence of samples {y n } n∈Z ∈ R Z of polynomial growth, find a multiply generated spline f of polynomial growth such thatIt is shown that the solution to this problem is unique over certain subspaces of the multiply generated spline space of polynomial growth.