{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:08:01Z","timestamp":1753880881741,"version":"3.41.2"},"reference-count":9,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2023,7]]},"abstract":"<jats:p> A multiwavelet is typically constructed starting from a vector-valued function satisfying a matrix refinement equation. The approximation order of such a refinable function vector is related to the sum rules of order [Formula: see text] satisfied by the corresponding refinement mask. A refinable function vector can be obtained using cascade algorithm by constructing a refinement mask which satisfies the sum rules of order [Formula: see text] A standard pair associated with a refinement mask gives information about its spectral properties. In this paper, we present a procedure for constructing refinement masks satisfying the sum rules of order [Formula: see text], starting from standard pairs. How this helps in the construction of asymmetric multiwavelets using standard pairs is illustrated through examples. A sufficient condition on a standard pair and a necessary and sufficient condition on a left standard pair are established so that the corresponding refinement mask satisfies the sum rules of order [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0219691322500606","type":"journal-article","created":{"date-parts":[[2022,11,22]],"date-time":"2022-11-22T16:13:30Z","timestamp":1669133610000},"source":"Crossref","is-referenced-by-count":3,"title":["Standard pairs and construction of multiwavelets using refinement masks satisfying sum rules of order one"],"prefix":"10.1142","volume":"21","author":[{"given":"P.","family":"Poornima","sequence":"first","affiliation":[{"name":"Department of Mathematics, National Institute of Technology, Tiruchirappalli 620015, Tamil Nadu, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6122-6455","authenticated-orcid":false,"given":"K.","family":"Murugesan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, National Institute of Technology, Tiruchirappalli 620015, Tamil Nadu, India"}]}],"member":"219","published-online":{"date-parts":[[2022,12,24]]},"reference":[{"key":"S0219691322500606BIB001","series-title":"Computer Science and Applied Mathematics","volume-title":"Matrix Polynomials","author":"Gohberg I.","year":"1982"},{"key":"S0219691322500606BIB002","first-page":"363","volume":"2","author":"Heil C.","year":"1996","journal-title":"J. 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Math."}],"container-title":["International Journal of Wavelets, Multiresolution and Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219691322500606","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,3]],"date-time":"2023-07-03T08:43:22Z","timestamp":1688373802000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0219691322500606"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,24]]},"references-count":9,"journal-issue":{"issue":"04","published-print":{"date-parts":[[2023,7]]}},"alternative-id":["10.1142\/S0219691322500606"],"URL":"https:\/\/doi.org\/10.1142\/s0219691322500606","relation":{},"ISSN":["0219-6913","1793-690X"],"issn-type":[{"type":"print","value":"0219-6913"},{"type":"electronic","value":"1793-690X"}],"subject":[],"published":{"date-parts":[[2022,12,24]]},"article-number":"2250060"}}