Multiresolution analysis for compactly supported interpolating tensor product wavelets

Abstract

We construct multidimensional interpolating tensor product multiresolution analyses (MRA's) of the function spaces C0(ℝn, K), K = ℝ or K = ℂ, consisting of real or complex valued functions on ℝn vanishing at infinity and the function spaces Cu(ℝn, K) consisting of bounded and uniformly continuous functions on ℝn. We also construct an interpolating dual MRA for both of these spaces. The theory of the tensor products of Banach spaces is used. We generalize the Besov space norm equivalence from the one-dimensional case to our n-dimensional construction.