Multiresolution Analysis for Compactly Supported Interpolating Tensor Product Wavelets (long version)

Details Multiresolution Analysis for Compactly Supported Interpolating Tensor Product Wavelets (long version) Multiresolution Analysis for Compactly Supported Interpolating Tensor Product Wavelets (long version)

2010-05-19

arxiv.org/abs/1005.3371v2

Mathematics

Functional Analysis

82 pages

Scientific paper

We construct a one-dimensional interpolating multiresolution analysis (MRA) of C0(R,K), K = R or K = C, and multidimensional interpolating tensor product MRAs of the function spaces C0(Rn,K) 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. The theory of the tensor products of Banach spaces is used. We also generalize the Besov space norm equivalence result from Donoho (1992, Interpolating Wavelet Transforms) for our n-dimensional construction.

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