Construction of the multi-wavelets on some smooth plane curves via length-preserving projection (Q2874061)

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curves are called by the authors ``multiplicity multi-resolution analysis'' and ``multiwavelets'', and again they do not cite at all the univariate construction they transport.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.