TY - JOUR
T1 - Stability of refinable functions, multiresolution analysis, and Haar bases
AU - Zhou, Ding-Xuan
PY - 1996/5
Y1 - 1996/5
N2 - 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.
AB - 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.
KW - Haar bases
KW - Multiresolution analysis
KW - Refinement equations
KW - Stability
KW - Wavelets
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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-0030537419&origin=recordpage
M3 - RGC 21 - Publication in refereed journal
SN - 0036-1410
VL - 27
SP - 891
EP - 904
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
IS - 3
ER -