{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T15:41:20Z","timestamp":1784130080842,"version":"3.55.0"},"reference-count":17,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2014,1]]},"abstract":"<jats:p> Based on the theory of the discrete multi-wavelets in the space L<jats:sup>2<\/jats:sup>(R), the theory of the discrete multi-wavelets in the space L<jats:sup>2<\/jats:sup>(C) is presented properly in this paper, where C denotes a smooth plane curve. Firstly, the length-preserving projection is constructed, and by the length-preserving projection, the multiplicity multi-resolution analysis in the space L<jats:sup>2<\/jats:sup>(C) is defined properly and we define the dilation operator and translation operator in the space L<jats:sup>2<\/jats:sup>(C). Then, the two-scale refinement equations of multi-scaling function and multi-wavelet in the space L<jats:sup>2<\/jats:sup>(C) is deduced by using length-preserving mapping, the orthogonality is discussed, and the decomposition and reconstruction algorithm is computed. Finally, the example is given. <\/jats:p>","DOI":"10.1142\/s0219691314500052","type":"journal-article","created":{"date-parts":[[2013,12,1]],"date-time":"2013-12-01T22:47:07Z","timestamp":1385938027000},"page":"1450005","source":"Crossref","is-referenced-by-count":6,"title":["CONSTRUCTION OF THE MULTI-WAVELETS ON SOME SMOOTH PLANE CURVES VIA LENGTH-PRESERVING PROJECTION"],"prefix":"10.1142","volume":"12","author":[{"given":"BAOQIN","family":"WANG","sequence":"first","affiliation":[{"name":"School of Mathematical Science, Xinjiang Normal University, Urumqi, Xinjiang 830054, P. R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"GANG","family":"WANG","sequence":"additional","affiliation":[{"name":"School of Mathematical Science, Xinjiang Normal University, Urumqi, Xinjiang 830054, P. R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"XIAOHUI","family":"ZHOU","sequence":"additional","affiliation":[{"name":"School of Mathematical Science, Xinjiang Normal University, Urumqi, Xinjiang 830054, P. R. 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