{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T08:59:28Z","timestamp":1777366768563,"version":"3.51.4"},"reference-count":16,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2008,3]]},"abstract":"<jats:p>For any \u03d5(t) in L<jats:sup>2<\/jats:sup>(\u211d), let V(\u03d5) be the closed shift invariant subspace of L<jats:sup>2<\/jats:sup>(\u211d) spanned by integer translates {\u03d5(t - n) : n \u2208 \u2124} of \u03d5(t). Assuming that \u03d5(t) is a frame or a Riesz generator of V(\u03d5), we first find conditions under which V(\u03d5) becomes a reproducing kernel Hilbert space. We then find necessary and sufficient conditions under which an irregular or a regular shifted sampling expansion formula holds on V(\u03d5) and obtain truncation error estimates of the sampling series. We also find a sufficient condition for a function in L<jats:sup>2<\/jats:sup>(\u211d) that belongs to a sampling subspace of L<jats:sup>2<\/jats:sup>(\u211d). Several illustrating examples are also provided.<\/jats:p>","DOI":"10.1142\/s021969130800232x","type":"journal-article","created":{"date-parts":[[2008,3,25]],"date-time":"2008-03-25T12:05:59Z","timestamp":1206446759000},"page":"223-248","source":"Crossref","is-referenced-by-count":23,"title":["SAMPLING EXPANSION IN SHIFT INVARIANT SPACES"],"prefix":"10.1142","volume":"06","author":[{"given":"J. M.","family":"KIM","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon, 305-701, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"K. H.","family":"KWON","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon, 305-701, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1080\/01630569408816545"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1006\/jfan.1994.1003"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1109\/78.720386"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2002.802646"},{"key":"rf5","volume-title":"An Introduction to Wavelets","author":"Chui C. K.","year":"1992"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-8224-8"},{"key":"rf7","volume-title":"Introduction to the Theory of Distributions","author":"Friedlander G.","year":"1998"},{"key":"rf8","first-page":"703","volume":"30","author":"Garc\u00eda A. G.","journal-title":"J. Math. Anal. Appl."},{"key":"rf9","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198596998.001.0001","volume-title":"Sampling Theory in Fourier and Signal Analysis: Foundations","author":"Higgins J. R.","year":"1996"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1142\/S0219691307002038"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1109\/78.258079"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1995-056-1"},{"key":"rf13","first-page":"223","volume":"48","author":"Sun W.","journal-title":"IEEE Trans. Signal Process."},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1109\/18.119745"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1007\/BF01259375"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1142\/S021969130500083X"}],"container-title":["International Journal of Wavelets, Multiresolution and Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021969130800232X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,24]],"date-time":"2024-02-24T02:09:48Z","timestamp":1708740588000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021969130800232X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,3]]},"references-count":16,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[2008,3]]}},"alternative-id":["10.1142\/S021969130800232X"],"URL":"https:\/\/doi.org\/10.1142\/s021969130800232x","relation":{},"ISSN":["0219-6913","1793-690X"],"issn-type":[{"value":"0219-6913","type":"print"},{"value":"1793-690X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,3]]}}}