Haar{type Orthonormal Wavelet Bases in R 2
نویسنده
چکیده
K.-H. Grr ochenig and A. Haas asked whether for every expanding integer matrix A 2 M n (Z) there is a Haar-type orthonormal wavelet basis having dilation factor A and translation lattice Z n. They proved that this is the case when the dimension n = 1. This paper shows that this is also the case when the dimension n = 2.
منابع مشابه
Some simple Haar–type wavelets in higher dimensions
An orthonormal wavelet system in R, d ∈ N, is a countable collection of functions {ψ j,k}, j ∈ Z, k ∈ Z, ` = 1, . . . , L, of the form ψ j,k(x) = | deta|−j/2ψ`(a−jx− k) ≡ (Daj Tk ψ)(x) that is an orthonormal basis for L2(Rd), where a ∈ GLd(R) is an expanding matrix. The first such system to be discovered (almost one hundred years ago) is the Haar system for which L = d = 1, ψ1(x) = ψ(x) = χ[0,1...
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