Construction of the multi-wavelets on some smooth plane curves via length-preserving projection
type: Item
instance of: scholarly article
zbMATH Open document ID: 1286.42054
DOI: 10.1142/S0219691314500052
author: Baoqin Wang
author: Gang Wang
author: Xiaohui Zhou
published in: International Journal of Wavelets, Multiresolution and Information Processing
publication date: 2014-01-28T00:00:00Z
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 65T60
zbMATH DE Number: 6251186
zbMATH Keywords: length-preserving projection
zbMATH Keywords: multiplicity multi-resolution analysis
zbMATH Keywords: wavelet on the manifold
MaRDI profile type: Publication
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title: Construction of the multi-wavelets on some smooth plane curves via length-preserving projection
review text: The construction of length preserving maps and the transportation of wavelets from \(\mathbb R\) to planar curves, presented in this paper, is based on the ideas in [\textit{D. Rosca}, Appl. Comput. Harmon. Anal. 30, No. 2, 262--272 (2011; Zbl 1213.42155)] for area preserving maps for surfaces of revolution, without mentioning it explicitly.NEWLINENEWLINEIn fact, the authors follow step by step the constructions in [loc. cit.], some text being reproduced verbatim (sometimes with mistakes, writing e.g. Reisz instead of Riesz). In the present paper, the multiresolution analysis and wavelets transported from \(\mathbb R\) on planar curves are called by the authors ``multiplicity multi-resolution analysis'' and ``multiwavelets'', and again they do not cite at all the univariate construction they transport. Instead, four papers by Y. Y. Tang, the editor-in-chief, are quoted, which have NOTHING to do with the topic of the present article.
reviewed by: Daniela Roşca
description: scientific article; zbMATH DE number 6251186