Multiresolution analysis for compactly supported interpolating tensor product wavelets

摘要

We construct multidimensional interpolating tensor product multiresolution analyses (MRA's) of the function spaces C-0(R-n, K), K = R or K = C, consisting of real or complex valued functions on Rn vanishing at infinity and the function spaces C-u(R-n, 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.