{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,27]],"date-time":"2024-03-27T11:18:00Z","timestamp":1711538280070},"reference-count":17,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2012,3]]},"abstract":"<jats:p> Gabardo and Nashed have studied nonuniform multiresolution analysis based on the theory of spectral pairs in a series of papers, see Refs. 4 and 5. Farkov,<jats:sup>3<\/jats:sup> has extended the notion of multiresolution analysis on locally compact Abelian groups and constructed the compactly supported orthogonal p-wavelets on L<jats:sup>2<\/jats:sup>(\u211d<jats:sub>+<\/jats:sub>). We have considered the nonuniform multiresolution analysis on positive half-line. The associated subspace V<jats:sub>0<\/jats:sub> of L<jats:sup>2<\/jats:sup>(\u211d<jats:sub>+<\/jats:sub>) has an orthonormal basis, a collection of translates of the scaling function \u03c6 of the form {\u03c6(x \u2296 \u03bb)}<jats:sub>\u03bb\u2208\u039b<jats:sub>+<\/jats:sub><\/jats:sub> where \u039b<jats:sub>+<\/jats:sub> = {0, r\/N} + \u2124<jats:sub>+<\/jats:sub>, N &gt; 1 (an integer) and r is an odd integer with 1 \u2264 r \u2264 2N - 1 such that r and N are relatively prime and \u2124<jats:sub>+<\/jats:sub> is the set of non-negative integers. We find the necessary and sufficient condition for the existence of associated wavelets and derive the analogue of Cohen's condition for the nonuniform multiresolution analysis on the positive half-line. <\/jats:p>","DOI":"10.1142\/s021969131250018x","type":"journal-article","created":{"date-parts":[[2012,2,15]],"date-time":"2012-02-15T02:25:24Z","timestamp":1329272724000},"page":"1250018","source":"Crossref","is-referenced-by-count":13,"title":["WAVELETS ASSOCIATED WITH NONUNIFORM MULTIRESOLUTION ANALYSIS ON POSITIVE HALF-LINE"],"prefix":"10.1142","volume":"10","author":[{"family":"MEENAKSHI","sequence":"first","affiliation":[{"name":"Department of Mathematics, Lajpat Rai DAV College, Jagraon, Punjab, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.","family":"MANCHANDA","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Guru Nanak Dev University, Amritsar, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. H.","family":"SIDDIQI","sequence":"additional","affiliation":[{"name":"School of Engineering and Technology, Sharda University, Greater Noida, India"},{"name":"Sultan Qaboos University, Muscat, Oman"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,5]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1142\/S0219691309003112"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970104"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1142\/S0219691311004195"},{"key":"rf5","first-page":"593","volume":"74","author":"Fridli S.","journal-title":"Acta Sci. Math. 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