{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,14]],"date-time":"2025-11-14T10:36:06Z","timestamp":1763116566285},"reference-count":12,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p> According to the theory of wavelet analysis on [Formula: see text], the wavelet analysis on a smooth surface [Formula: see text] with nonzero constant Gaussian curvature will be discussed systematically in this paper. First, a general area-preserving projection from a smooth surface to the plane will be presented by the Gaussian projection and the area-preserving projection on the sphere. Then the continuous wavelet transform and its inverse transform on a smooth surface [Formula: see text] with nonzero constant Gaussian curvature will be discussed by a general area-preserving projection, relative dilation operator and translation operator. Further, according to the multi-resolution analysis on a smooth surface, the discrete wavelet transform and relative properties will be investigated systematically, including the two-scale equations of the wavelet function, orthogonality and so on. Finally, two numerical examples will be given. <\/jats:p>","DOI":"10.1142\/s0219691318500078","type":"journal-article","created":{"date-parts":[[2017,10,26]],"date-time":"2017-10-26T08:42:26Z","timestamp":1509007346000},"page":"1850007","source":"Crossref","is-referenced-by-count":7,"title":["Wavelet analysis on some smooth surface with nonzero constant Gaussian curvature"],"prefix":"10.1142","volume":"16","author":[{"given":"Xiaohui","family":"Zhou","sequence":"first","affiliation":[{"name":"School of Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, P. R. China"},{"name":"Department of Applied Mathematics, Zhejiang University of Finance and Economics Dongfang College, Jiaxing, Zhejiang 314400, P. R. China"}]},{"given":"Baoqin","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics Science, Xinjiang Normal University, Urumqi, Xinjiang 830054, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2018,1,30]]},"reference":[{"key":"S0219691318500078BIB001","doi-asserted-by":"publisher","DOI":"10.1142\/S0219691308002288"},{"key":"S0219691318500078BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2009.10.002"},{"key":"S0219691318500078BIB003","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970104"},{"key":"S0219691318500078BIB004","series-title":"Fachbereich Mathematik und Informatikder","volume-title":"Interpolating Scaling Vectors and Multiwavelets in Rd","author":"Koch K.","year":"2006"},{"key":"S0219691318500078BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s00041-006-6014-z"},{"key":"S0219691318500078BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2010.09.008"},{"key":"S0219691318500078BIB007","doi-asserted-by":"publisher","DOI":"10.1142\/S0219691315500071"},{"key":"S0219691318500078BIB008","doi-asserted-by":"publisher","DOI":"10.1142\/S0219691315500277"},{"issue":"6","key":"S0219691318500078BIB009","first-page":"877","volume":"42","author":"Wang B.","year":"2012","journal-title":"J. Northwest Univ. (Nat. Sci. Edn.)"},{"key":"S0219691318500078BIB010","doi-asserted-by":"publisher","DOI":"10.1109\/TCSVT.2014.2306031"},{"key":"S0219691318500078BIB011","doi-asserted-by":"publisher","DOI":"10.1142\/S0219691311004389"},{"key":"S0219691318500078BIB012","doi-asserted-by":"publisher","DOI":"10.1142\/S0218001409007260"}],"container-title":["International Journal of Wavelets, Multiresolution and Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219691318500078","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T19:32:01Z","timestamp":1565119921000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219691318500078"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":12,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2018,1,30]]},"published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1142\/S0219691318500078"],"URL":"https:\/\/doi.org\/10.1142\/s0219691318500078","relation":{},"ISSN":["0219-6913","1793-690X"],"issn-type":[{"value":"0219-6913","type":"print"},{"value":"1793-690X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]}}}