Multiresolution analysis for compactly supported interpolating tensor product wavelets

Abstract

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 R n vanishing at infinity and the function spaces Cu(R n , K) consisting of bounded and uniformly continuous functions on R n . 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.

Electronic structure calculations with interpolating tensor product wavelet basis

“…Compactly supported interpolating wavelets have been generalized to multiple dimensions in Refs. [5], [6], and [7]. Fukuda, Kinoshita, and Suzuki [8] have studied unconditional convergence of wavelet expansions.…”

“…The notation for wavelet basis functions and filters is similar to Refs. [5] and [6]. The computation of matrix elements is similar to Ref.…”