{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T08:50:18Z","timestamp":1648630218770},"reference-count":8,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2007,7]]},"abstract":"<jats:p> We generalize the inequality |P(z)|<jats:sup>2<\/jats:sup> + |P(-z)|<jats:sup>2<\/jats:sup> \u2264 1 (Ref. 1) to the inequality |P(z<jats:sub>1<\/jats:sub>, z<jats:sub>2<\/jats:sub>)|<jats:sup>2<\/jats:sup> + |P(-z<jats:sub>1<\/jats:sub>, z<jats:sub>2<\/jats:sub>)|<jats:sup>2<\/jats:sup> + |P(z<jats:sub>1<\/jats:sub>, -z<jats:sub>2<\/jats:sub>)|<jats:sup>2<\/jats:sup> + |P(-z<jats:sub>1<\/jats:sub>, -z<jats:sub>2<\/jats:sub>)|<jats:sup>2<\/jats:sup> \u2264 1 in L<jats:sup>2<\/jats:sup>(\u211d<jats:sup>2<\/jats:sup>); and construct compactly supported tight frames with good symmetry and dilation matrix 2I under the condition that both the low-pass filter and high-pass filters are unknown. <\/jats:p>","DOI":"10.1142\/s0219691307001926","type":"journal-article","created":{"date-parts":[[2007,7,5]],"date-time":"2007-07-05T05:38:16Z","timestamp":1183613896000},"page":"613-625","source":"Crossref","is-referenced-by-count":2,"title":["CONSTRUCTION FOR A CLASS OF SMOOTH TIGHT FRAMES IN L<sup>2<\/sup>(\u211d<sup>2<\/sup>)"],"prefix":"10.1142","volume":"05","author":[{"given":"HAIHUI","family":"WANG","sequence":"first","affiliation":[{"name":"LMIB, Department of Mathematics, Beihang University, Beijing, 100083, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"LIZHONG","family":"PENG","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Peking University, Beijing, 100871, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1006\/acha.2000.0301"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1006\/jfan.1996.3079"},{"key":"rf3","first-page":"1309","volume":"47","author":"Basu S.","journal-title":"IEEE Trans."},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2006.04.001"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/S1063-5203(02)00511-0"},{"key":"rf8","first-page":"445","volume":"46","author":"Wang H.","journal-title":"Sci. China F"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1109\/18.650985"},{"key":"rf13","first-page":"203","volume":"10","author":"Goynal V. K.","journal-title":"J. Appl. Comput. Harmon. Anal."}],"container-title":["International Journal of Wavelets, Multiresolution and Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219691307001926","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T13:22:07Z","timestamp":1565184127000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219691307001926"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,7]]},"references-count":8,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[2007,7]]}},"alternative-id":["10.1142\/S0219691307001926"],"URL":"https:\/\/doi.org\/10.1142\/s0219691307001926","relation":{},"ISSN":["0219-6913","1793-690X"],"issn-type":[{"value":"0219-6913","type":"print"},{"value":"1793-690X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,7]]}}}