Convergence of cascade algorithms in Sobolev spaces and integrals of wavelets |
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| Authors: | Rong-Qing Jia Qingtang Jiang SL Lee |
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| Institution: | (1) Department of Mathematical Sciences, University of Alberta, Edmonton, Canada T6G 2G1 , CA;(2) Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260; e-mail: matleesl@math.nus.edu.sg , SG |
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| Abstract: | Summary. The cascade algorithm with mask a and dilation M generates a sequence by the iterative process
from a starting function 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.
Received May 5, 1999 / Revised version received June 24, 1999 / Published online June 20, 2001 |
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| Keywords: | Mathematics Subject Classification (1991): 42C15 65D20 41A15 65R10 42C05 |
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