Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 50, Issue 8-9, Pages 1191-1210Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2005.07.001
Keywords
harmonic wavelets; connection coefficients; refinable integrals; PDE
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In this paper, harmonic wavelets, which are analytically defined and band limited, are studied, together with their differentiable properties. Harmonic wavelets were recently applied to the solution of evolution problems and, more generally, to describe evolution operators. In order to consider the evolution of a solitary profile (and to focus on the localization property of wavelets), it seems to be more expedient to make use of functions with limited compact support (either in space or in frequency). The connection coefficients of harmonic wavelets are explicitly computed (in the following) at any order, and characterized by some recursive formulas. In particular, they are functionally and finitely defined by a simple formula for any order of the basis derivatives. (c) 2005 Elsevier Ltd. All rights reserved.
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