{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:13:52Z","timestamp":1760242432618,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2017,7,6]],"date-time":"2017-07-06T00:00:00Z","timestamp":1499299200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we generalize the family of Deslauriers\u2013Dubuc\u2019s interpolatory masks from dimension one to arbitrary dimensions with respect to the quincunx dilation matrices, thereby providing a family of quincunx fundamental refinable functions in arbitrary dimensions. We show that a family of unique quincunx interpolatory masks exists and such a family of masks is of real value and has the full-axis symmetry property. In dimension     d = 2    , we give the explicit form of such unique quincunx interpolatory masks, which implies the nonnegativity property of such a family of masks.<\/jats:p>","DOI":"10.3390\/axioms6030020","type":"journal-article","created":{"date-parts":[[2017,7,6]],"date-time":"2017-07-06T10:55:45Z","timestamp":1499338545000},"page":"20","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Quincunx Fundamental Refinable Functions in Arbitrary Dimensions"],"prefix":"10.3390","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7238-0143","authenticated-orcid":false,"given":"Xiaosheng","family":"Zhuang","sequence":"first","affiliation":[{"name":"Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong, Hong Kong"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,7,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1177","DOI":"10.1137\/S0036141097294032","article-title":"Multivariate refinement equations and convergence of subdivision schemes","volume":"29","author":"Han","year":"1998","journal-title":"SIAM J. 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Theory"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/6\/3\/20\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:41:42Z","timestamp":1760208102000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/6\/3\/20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7,6]]},"references-count":21,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2017,9]]}},"alternative-id":["axioms6030020"],"URL":"https:\/\/doi.org\/10.3390\/axioms6030020","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2017,7,6]]}}}