{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T15:06:51Z","timestamp":1761059211074},"reference-count":24,"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":[[2012,1]]},"abstract":"<jats:p> Let \u03c6 be a continuous function in L<jats:sup>2<\/jats:sup>(\u211d) such that the sequence {\u03c6(t - n)}<jats:sub>n\u2208\u2124<\/jats:sub> is a frame sequence in L<jats:sup>2<\/jats:sup>(\u211d) and assume that the shift-invariant space V(\u03c6) generated by \u03c6 has a multi-banded spectrum \u03c3(V). The main aim in this paper is to derive a multi-channel sampling theory for the shift-invariant space V(\u03c6). By using a type of Fourier duality between the spaces V(\u03c6) and L<jats:sup>2<\/jats:sup>[0, 2\u03c0] we find necessary and sufficient conditions allowing us to obtain stable multi-channel sampling expansions in V(\u03c6). <\/jats:p>","DOI":"10.1142\/s0219691311004456","type":"journal-article","created":{"date-parts":[[2011,7,14]],"date-time":"2011-07-14T01:47:05Z","timestamp":1310608025000},"page":"1250003","source":"Crossref","is-referenced-by-count":10,"title":["MULTI-CHANNEL SAMPLING ON SHIFT-INVARIANT SPACES WITH FRAME GENERATORS"],"prefix":"10.1142","volume":"10","author":[{"given":"A. G.","family":"GARCIA","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidad Carlos III de Madrid, Leganes, Madrid, 28911, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J. M.","family":"KIM","sequence":"additional","affiliation":[{"name":"Department of Bio and Brain Engineering, KAIST, Daejeon 305-701, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"K. H.","family":"KWON","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, KAIST, Daejeon 305-701, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G. J.","family":"YOON","sequence":"additional","affiliation":[{"name":"National Institute of Mathematical Sciences, Daejeon 305-340, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,5]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144501386986"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/s00041-005-4003-3"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1080\/01630569408816545"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1109\/78.720386"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-8224-8"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1109\/78.558473"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1142\/S0219691308002264"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2004.824022"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2007.03.083"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2005.10.001"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1142\/S021969130700180X"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2004.11.058"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1142\/S0219691307002038"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1109\/78.258079"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1017\/S0013091500006076"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2009.12.005"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1142\/S021969130800232X"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2007.11.005"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1977.1084284"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1109\/5.843002"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1109\/82.718806"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2003.819001"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1109\/18.119745"},{"key":"rf24","doi-asserted-by":"publisher","DOI":"10.1007\/BF01259375"}],"container-title":["International Journal of Wavelets, Multiresolution and Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219691311004456","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T18:31:57Z","timestamp":1565116317000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219691311004456"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":24,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2012,5]]},"published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1142\/S0219691311004456"],"URL":"https:\/\/doi.org\/10.1142\/s0219691311004456","relation":{},"ISSN":["0219-6913","1793-690X"],"issn-type":[{"value":"0219-6913","type":"print"},{"value":"1793-690X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,1]]}}}