Stability of refinable functions, multiresolution analysis, and Haar bases

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  • Ding-Xuan Zhou


Original languageEnglish
Pages (from-to)891-904
Journal / PublicationSIAM Journal on Mathematical Analysis
Issue number3
Publication statusPublished - May 1996
Externally publishedYes


The stability of the integer translates of a univariate refinable function is characterized in terms of the mask sequence in the corresponding k-scale (k ≥ 2) refinement equation. We show that the stability and refinement of some kinds of basis functions lead to a multiresolution analysis in LP(ℝs)(1 ≤ p ≤ ∞, s ∈ ℕ) based on general lattices. As an application we determine explicitly all those multiresolution analyses in L2(ℝ) associated with (ℤ, k) whose scaling functions are characteristic functions.

Research Area(s)

  • Haar bases, Multiresolution analysis, Refinement equations, Stability, Wavelets

Citation Format(s)