{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:57:49Z","timestamp":1760245069736,"version":"3.30.2"},"reference-count":14,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2004,9]]},"abstract":"<jats:p>A Generalized Multiresolution Analysis (GMRA) associated with a wavelet is a sequence of nested subspaces of the function space \u2112<jats:sup>2<\/jats:sup>(\u211d), with specific properties, and arranged in such a way that each of the subspaces corresponds to a scale 2<jats:sup>m<\/jats:sup>over all time-shifts n. These subspaces can be expressed in terms of a generating-wandering subspace \u2014 of the dyadic-scaling operator \u2014 spanned by orthonormal wavelet-functions \u2014 generated from the wavelet. In this paper we show that a GMRA can also be expressed in terms of subspaces for each time-shift n over all scales 2<jats:sup>m<\/jats:sup>. This is achieved by means of \"elementary\" reducing subspaces of the dyadic-scaling operator. Consequently, Time-Shifts GMRA associated with wavelets, as well as \"sub-GMRA\" associated with \"sub-wavelets\" will then be introduced.<\/jats:p>","DOI":"10.1142\/s0219691304000494","type":"journal-article","created":{"date-parts":[[2004,8,30]],"date-time":"2004-08-30T11:36:17Z","timestamp":1093865777000},"page":"237-248","source":"Crossref","is-referenced-by-count":6,"title":["TIME-SHIFTS GENERALIZED MULTIRESOLUTION ANALYSIS OVER DYADIC-SCALING REDUCING SUBSPACES"],"prefix":"10.1142","volume":"02","author":[{"given":"NHAN","family":"LEVAN","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, University of California in Los Angeles, Los Angeles, CA 90024-1594, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"CARLOS S.","family":"KUBRUSLY","sequence":"additional","affiliation":[{"name":"Catholic University of Rio de Janeiro, 22453-900, Rio de Janeiro, RJ, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4754(99)00009-9"},{"key":"rf2","first-page":"553","volume":"5","author":"Baggett L. W.","journal-title":"J. Fourier Anal. Appl."},{"volume-title":"An Introduction to Wavelets","year":"1992","author":"Chui C. K.","key":"rf3"},{"key":"rf4","series-title":"Mem. Amer. Math. Soc.","volume-title":"Wandering Vectors for Unitary Systems and Orthogonal Wavelets","volume":"134","author":"Dai X.","year":"1998"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1993-1117215-0"},{"key":"rf6","first-page":"102","volume":"208","author":"Halmos P. R.","journal-title":"J. Reine Angew. Math."},{"key":"rf7","first-page":"41","volume":"14","author":"Kubrusly C. S.","journal-title":"Adv. Math. Sci. Appl."},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4754(03)00037-5"},{"volume-title":"Scattering Theory","year":"1967","author":"Lax P. D.","key":"rf9"},{"key":"rf10","first-page":"69","volume":"315","author":"Mallat S. G.","journal-title":"Trans. Amer. Math. Soc."},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1109\/34.192463"},{"volume-title":"A Wavelet Tour of Signal Processing","year":"1998","author":"Mallat S. G.","key":"rf12"},{"key":"rf14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4171\/rmi\/22","volume":"2","author":"Lemari\u00e9 P.-G.","journal-title":"Rev. Mat. Iber."},{"volume-title":"Harmonic Analysis of Operators on Hilbert Space","year":"1970","author":"Sz-Nagy B.","key":"rf15"}],"container-title":["International Journal of Wavelets, Multiresolution and Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219691304000494","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,18]],"date-time":"2024-12-18T12:41:26Z","timestamp":1734525686000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219691304000494"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,9]]},"references-count":14,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[2004,9]]}},"alternative-id":["10.1142\/S0219691304000494"],"URL":"https:\/\/doi.org\/10.1142\/s0219691304000494","relation":{},"ISSN":["0219-6913","1793-690X"],"issn-type":[{"type":"print","value":"0219-6913"},{"type":"electronic","value":"1793-690X"}],"subject":[],"published":{"date-parts":[[2004,9]]}}}