{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:13:03Z","timestamp":1753884783998,"version":"3.41.2"},"reference-count":44,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12461016"],"award-info":[{"award-number":["12461016"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Ningxia Higher Education","award":["NXYLXK2017B09"],"award-info":[{"award-number":["NXYLXK2017B09"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2025,7]]},"abstract":"<jats:p> The superframe theory defined on half of the real line [Formula: see text] has extensive applications in multiplexing-based fields. Due to [Formula: see text] forming a group under Walsh addition \u201c\u2295\u201d, a \u201c\u2295\u201d-based Walsh wavelet analysis has potential advantages over classical wavelet analysis. This paper addresses (weak) nonhomogeneous wavelet dual superframes for Walsh-reducing subspace of vector-valued Sobolev space [Formula: see text] with [Formula: see text] and [Formula: see text]. We, in this paper, characterize Walsh-reducing subspace of [Formula: see text] and its (weak) nonhomogeneous wavelet dual superframes in the framework of Walsh wavelet analysis. Also some examples are provided. <\/jats:p>","DOI":"10.1142\/s0219691325500092","type":"journal-article","created":{"date-parts":[[2025,3,20]],"date-time":"2025-03-20T06:49:04Z","timestamp":1742453344000},"source":"Crossref","is-referenced-by-count":0,"title":["Nonhomogeneous wavelet dual superframes for reducing subspace of vector-valued Sobolev space on half of the real line"],"prefix":"10.1142","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5248-5271","authenticated-orcid":false,"given":"Yan","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hai-Yang","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, P. R. 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