Please use this identifier to cite or link to this item: https://doi.org/10.1007/s002110100265
Title: Convergence of cascade algorithms in Sobolev spaces and integrals of wavelets
Authors: Jia, R.-Q.
Jiang, Q.
Lee, S.L. 
Issue Date: May-2002
Source: Jia, R.-Q., Jiang, Q., Lee, S.L. (2002-05). Convergence of cascade algorithms in Sobolev spaces and integrals of wavelets. Numerische Mathematik 91 (3) : 453-473. ScholarBank@NUS Repository. https://doi.org/10.1007/s002110100265
Abstract: The cascade algorithm with mask a and dilation M generates a sequence φn, n = 1, 2,..., by the iterative process φn(x) = ∑αεℤs a(α)φn-1(Mx - α) x ε ℝs, from a starting function φ0, where M is a dilation matrix. A complete characterization is given for the strong convergence of cascade algorithms in Sobolev spaces for the case in which M is isotropic. The results on the convergence of cascade algorithms are used to deduce simple conditions for the computation of integrals of products of derivatives of refinable functions and wavelets.
Source Title: Numerische Mathematik
URI: http://scholarbank.nus.edu.sg/handle/10635/103071
ISSN: 0029599X
DOI: 10.1007/s002110100265
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