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Multiresolution analysis for compactly supported interpolating tensor product wavelets

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Details

Original languageEnglish
Article number1550010
Number of pages36
JournalInternational Journal of Wavelets Multiresolution and Information ProcessIng
Volume13
Issue number2
DOIs
Publication statusPublished - 6 Mar 2015
Publication typeA1 Journal article-refereed

Abstract

We construct multidimensional interpolating tensor product multiresolution analyses (MRA's) of the function spaces C<inf>0</inf>(R<sup>n</sup>,K), K = R or K = C, consisting of real or complex valued functions on R<sup>n</sup> vanishing at infinity and the function spaces Cu(R<sup>n</sup>,K) consisting of bounded and uniformly continuous functions on R<sup>n</sup>. 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.

Keywords

  • Besov space, injective tensor norm, Interpolating wavelets, multiresolution analysis, multivariate wavelets, projective tensor norm, tensor Product

Publication forum classification

Field of science, Statistics Finland