Spline wavelets on the unit circle
type: Item
instance of: scholarly article
title: Spline wavelets on the unit circle
zbMATH Open document ID: 0877.65006
DOI: 10.1007/BF03322168
published in: Results in Mathematics
publication date: 1997-12-08T00:00:00Z
review text: Spline function spaces over refined partitions form an excellent setting for multiresolution analysis which in turn leads to wavelet construction. The author considers complex spline function spaces defined on the unit circle with equispaced nodes and obtains an orthonormal basis in terms of the B-splines [cf. \textit{M. Kamada}, \textit{K. Toraichi} and \textit{R. Mori}, J. Approximation Theory 55, No. 1, 27-34 (1988; Zbl 0679.41007)]. Two scale equations for such orthonormal bases are also derived. Thus a decomposition of the space of square integrable functions over \([0,2\pi]\) into different orthogonal subspaces is obtained. The decomposition and reconstruction formulas each consist of only two terms.
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 65E05
Mathematics Subject Classification ID: 30E10
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 65T60
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 1029207
zbMATH Keywords: spline function spaces
zbMATH Keywords: spline wavelets
zbMATH Keywords: multiresolution analysis
zbMATH Keywords: orthonormal basis
zbMATH Keywords: decomposition
zbMATH Keywords: reconstruction
author: Hanlin Chen
reviewed by: H. P. Dikshit
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1029207