{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:13:29Z","timestamp":1753881209658,"version":"3.41.2"},"reference-count":16,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,7,9]],"date-time":"2012-07-09T00:00:00Z","timestamp":1341792000000},"content-version":"vor","delay-in-days":190,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"Doctoral Program Foundation of the Ministry of China","award":["200810780002","10971039"],"award-info":[{"award-number":["200810780002","10971039"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["200810780002","10971039"],"award-info":[{"award-number":["200810780002","10971039"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>Let <jats:bold>a<\/jats:bold>\u2009\u2009 = (<jats:italic>a<\/jats:italic><jats:sub>1<\/jats:sub>, <jats:italic>a<\/jats:italic><jats:sub>2<\/jats:sub>, \u2026, <jats:italic>a<\/jats:italic><jats:sub><jats:italic>m<\/jats:italic><\/jats:sub>)\u2208<jats:italic>\u2102<\/jats:italic><jats:sup><jats:italic>m<\/jats:italic><\/jats:sup> be an <jats:italic>m<\/jats:italic>\u2010dimensional vector. Then, it can be identified with an <jats:italic>m<\/jats:italic> \u00d7 <jats:italic>m<\/jats:italic> circulant matrix. By using the theory of matrix\u2010valued wavelet analysis (Walden and  Serroukh, 2002), we discuss the vector\u2010valued multiresolution analysis. Also, we derive several different designs of finite length of vector\u2010valued filters. The corresponding scaling functions and wavelet functions are given. Specially, we deal with the construction of filters on symmetric matrix\u2010valued functions space.<\/jats:p>","DOI":"10.1155\/2012\/130939","type":"journal-article","created":{"date-parts":[[2012,7,9]],"date-time":"2012-07-09T21:18:19Z","timestamp":1341868699000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Constructions of Vector\u2010Valued Filters and Vector\u2010Valued Wavelets"],"prefix":"10.1155","volume":"2012","author":[{"given":"Jianxun","family":"He","sequence":"first","affiliation":[]},{"given":"Shouyou","family":"Huang","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,7,9]]},"reference":[{"key":"e_1_2_7_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-12-174584-4.50005-0"},{"key":"e_1_2_7_2_2","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970104"},{"key":"e_1_2_7_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(89)90055-4"},{"key":"e_1_2_7_4_2","doi-asserted-by":"publisher","DOI":"10.2307\/2154695"},{"key":"e_1_2_7_5_2","doi-asserted-by":"publisher","DOI":"10.1137\/0515056"},{"key":"e_1_2_7_6_2","doi-asserted-by":"publisher","DOI":"10.1137\/1031129"},{"key":"e_1_2_7_7_2","doi-asserted-by":"publisher","DOI":"10.2307\/2001373"},{"key":"e_1_2_7_8_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0219691305000804"},{"key":"e_1_2_7_9_2","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2001.0866"},{"key":"e_1_2_7_10_2","first-page":"159","volume-title":"Contemporary Math","author":"Xia X. 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