Abstract
In this chapter, we construct compactly supported (orthonormal) systems of wavelets for L2(Rd), d > 1. Each system is of the form
where Λ is a rank d lattice subgroup of Rd, M is a strictly expansive linear transformation with MΛ ⊂ Λ, and m = |detM|. The fundamental wavelets, ψs, 1 ≤ s ≤ m −1 are defined by functional equations having the form
where a s p are complex-valued functions having finite support on Λ and satisfy certain algebraic conditions, and the scaling function ϕ satisfies the scaling equation
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© 1998 Springer Science+Business Media New York
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Resnikoff, H.L., Wells, R.O. (1998). Higher-Dimensional Wavelet Systems. In: Wavelet Analysis. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0593-7_7
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DOI: https://doi.org/10.1007/978-1-4612-0593-7_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6830-7
Online ISBN: 978-1-4612-0593-7
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