Reconstruction of vector and tensor fields from sampled discrete data

amalgam space W (C,L2(R, T 1 1 )) which is locally continuous and globally L2. We show that the sampling or discretization operator R from S to l2(Z, T 1 1 ) is a bounded linear operator. We introduce the dilated spaces S∆ = D∆ S parametrized by the coarseness ∆, and show that the discretization operator is also bounded with a bounded inverse for any ∆ ∈ Zn. This allows us to represent discrete tensor field data in terms of continuous tensor fields in S∆, and to obtain continous representations with fast filtering algorithms.