{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,27]],"date-time":"2024-03-27T11:17:43Z","timestamp":1711538263172},"reference-count":26,"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":[[2015,7]]},"abstract":"<jats:p> A multiresolution analysis (MRA) on local fields of positive characteristic was defined by Shah and Abdullah for which the translation set is a discrete set which is not a group. In this paper, we continue the study based on this nonstandard setting and introduce vector-valued nonuniform multiresolution analysis (VNUMRA) where the associated subspace V<jats:sub>0<\/jats:sub> of L<jats:sup>2<\/jats:sup>(K, \u2102<jats:sup>M<\/jats:sup>) has an orthonormal basis of the form {\u03a6 (x - \u03bb)}<jats:sub>\u03bb\u2208\u039b<\/jats:sub> where \u039b = {0, r\/N} + \ud835\udcb5, N \u2265 1 is an integer and r is an odd integer such that r and N are relatively prime and \ud835\udcb5 = {u(n) : n \u2208 \u2115<jats:sub>0<\/jats:sub>}. We establish a necessary and sufficient condition for the existence of associated wavelets and derive an algorithm for the construction of VNUMRA on local fields starting from a vector refinement mask G(\u03be) with appropriate conditions. Further, these results also hold for Cantor and Vilenkin groups. <\/jats:p>","DOI":"10.1142\/s0219691315500290","type":"journal-article","created":{"date-parts":[[2015,6,9]],"date-time":"2015-06-09T23:32:02Z","timestamp":1433892722000},"page":"1550029","source":"Crossref","is-referenced-by-count":14,"title":["Vector-valued nonuniform multiresolution analysis on local fields"],"prefix":"10.1142","volume":"13","author":[{"given":"Firdous Ahmad","family":"Shah","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Kashmir, South Campus, Anantnag-192101, Jammu and Kashmir, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M. Younus","family":"Bhat","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Central University of Jammu, Jammu-180011, Jammu and Kashmir, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2015,7,28]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1515\/anly-2014-1247"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1515\/apam-2011-0016"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/BF02922099"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2006.03.097"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-8418-1"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1070\/IM2005v069n03ABEH000540"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1006\/jfan.1998.3253"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/216\/02963"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2004.02.026"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/j.jat.2008.08.008"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1137\/S0036141093248049"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/s00041-013-9301-6"},{"key":"rf13","first-page":"69","volume":"315","author":"Mallat S. 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