{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,18]],"date-time":"2024-06-18T16:37:52Z","timestamp":1718728672200},"reference-count":20,"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> A constructive algorithm based on the theory of spectral pairs for constructing nonuniform wavelet basis in [Formula: see text] was considered by Gabardo and Nashed [Nonuniform multiresolution analysis and spectral pairs, J. Funct. Anal. 158 (1998) 209\u2013241]. In this setting, the associated translation set is a spectrum [Formula: see text] which is not necessarily a group nor a uniform discrete set, given [Formula: see text] where [Formula: see text] (an integer) and [Formula: see text] is an odd integer with [Formula: see text] such that [Formula: see text] and [Formula: see text] are relatively prime and [Formula: see text] is the set of all integers. The objective of this paper is to construct nonuniform wavelet frame on local fields. A necessary condition and four sufficient conditions for nonuniform wavelet frame on local fields are given. <\/jats:p>","DOI":"10.1142\/s0219691318500054","type":"journal-article","created":{"date-parts":[[2017,11,21]],"date-time":"2017-11-21T08:09:02Z","timestamp":1511251742000},"page":"1850005","source":"Crossref","is-referenced-by-count":4,"title":["Necessary condition and sufficient conditions for nonuniform wavelet frames in L2(K)"],"prefix":"10.1142","volume":"16","author":[{"given":"M.","family":"Younus Bhat","sequence":"first","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":[[2018,1,30]]},"reference":[{"key":"S0219691318500054BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/BF02922099"},{"key":"S0219691318500054BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/S1063-5203(02)00511-0"},{"key":"S0219691318500054BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-8418-1"},{"key":"S0219691318500054BIB004","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1952-0047179-6"},{"key":"S0219691318500054BIB005","doi-asserted-by":"publisher","DOI":"10.1006\/jfan.1998.3253"},{"key":"S0219691318500054BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2005.10.077"},{"key":"S0219691318500054BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(02)00891-9"},{"key":"S0219691318500054BIB008","doi-asserted-by":"publisher","DOI":"10.1142\/S0219691309002751"},{"key":"S0219691318500054BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/s00041-001-0002-1"},{"key":"S0219691318500054BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2008.04.031"},{"key":"S0219691318500054BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/s00041-013-9301-6"},{"issue":"8","key":"S0219691318500054BIB012","first-page":"1463","volume":"82","author":"Pan J.","year":"1999","journal-title":"IEICE Trans. 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