{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T05:06:12Z","timestamp":1648962372749},"reference-count":25,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2014,3]]},"abstract":"<jats:p> We introduce the notion of dual-shift decomposition of an arbitrary Hilbert space, which is given in terms of two unilateral shifts. After ensuring conditions for the existence of it, such a decomposition is then constructed for the concrete space \u2112<jats:sup>2<\/jats:sup>[0, 1], on which the two unilateral shifts are parts of the dilation-by-2 and the translation-by-1 on \u2112<jats:sup>2<\/jats:sup>(\u211d). Using multiresolution analysis (MRA) of wavelet theory it is shown the existence of a Haar-system-type orthonormal basis for \u2112<jats:sup>2<\/jats:sup>[0, 1], which is combined with the dual-shift decomposition to yield a refined decomposition for \u2112<jats:sup>2<\/jats:sup>[0, 1]. <\/jats:p>","DOI":"10.1142\/s0219691314500143","type":"journal-article","created":{"date-parts":[[2013,12,16]],"date-time":"2013-12-16T02:43:06Z","timestamp":1387161786000},"page":"1450014","source":"Crossref","is-referenced-by-count":0,"title":["DUAL-SHIFT DECOMPOSITION AND WAVELETS"],"prefix":"10.1142","volume":"12","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":[[2014,3,2]]},"reference":[{"key":"rf1","first-page":"829","volume":"34","author":"Antoniou I.","journal-title":"Differ. 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