{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:17:57Z","timestamp":1753885077835,"version":"3.41.2"},"reference-count":10,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["20K03690"],"award-info":[{"award-number":["20K03690"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2022,1]]},"abstract":"<jats:p> We are concerned with the orthonormal wavelet [Formula: see text] in the Hardy space [Formula: see text] which is a closed subspace of [Formula: see text] without negative frequency components. It is well known that there does not exist an [Formula: see text]-wavelet such that [Formula: see text] is continuous on [Formula: see text] and satisfies [Formula: see text] for some [Formula: see text]. The aim of this paper is to find a critical decay rate in the existing [Formula: see text]-wavelet under the condition that [Formula: see text] is continuous on [Formula: see text]. Moreover, we also construct a concrete [Formula: see text]-wavelet having infinite vanishing moments. <\/jats:p>","DOI":"10.1142\/s0219691321500442","type":"journal-article","created":{"date-parts":[[2021,10,7]],"date-time":"2021-10-07T02:12:07Z","timestamp":1633572727000},"source":"Crossref","is-referenced-by-count":1,"title":["On the construction of the orthonormal wavelet in the Hardy space H2(\u211d)"],"prefix":"10.1142","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1057-1061","authenticated-orcid":false,"given":"Hirofumi","family":"Hashimoto","sequence":"first","affiliation":[{"name":"Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan"}]},{"given":"Tamotu","family":"Kinoshita","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan"}]}],"member":"219","published-online":{"date-parts":[[2021,10,6]]},"reference":[{"issue":"7","key":"S0219691321500442BIB001","first-page":"769","volume":"315","author":"Auscher P.","year":"1992","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. I Math."},{"key":"S0219691321500442BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/BF02921675"},{"key":"S0219691321500442BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0505-0"},{"key":"S0219691321500442BIB004","doi-asserted-by":"publisher","DOI":"10.4064\/ba52-2-7"},{"key":"S0219691321500442BIB005","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970104"},{"key":"S0219691321500442BIB006","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/45\/24\/244017"},{"key":"S0219691321500442BIB007","doi-asserted-by":"publisher","DOI":"10.1201\/9780367802349"},{"issue":"2","key":"S0219691321500442BIB008","first-page":"141","volume":"49","author":"Majchrowska G.","year":"2001","journal-title":"Bull. Polish Acad. Sci. Math."},{"key":"S0219691321500442BIB009","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1989-1008470-5"},{"key":"S0219691321500442BIB010","series-title":"Cambridge Studies in Advanced Mathematics","volume-title":"Wavelets and Operators","volume":"37","author":"Meyer Y.","year":"1992"}],"container-title":["International Journal of Wavelets, Multiresolution and Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219691321500442","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,2,17]],"date-time":"2022-02-17T05:48:02Z","timestamp":1645076882000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219691321500442"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,6]]},"references-count":10,"journal-issue":{"issue":"01","published-print":{"date-parts":[[2022,1]]}},"alternative-id":["10.1142\/S0219691321500442"],"URL":"https:\/\/doi.org\/10.1142\/s0219691321500442","relation":{},"ISSN":["0219-6913","1793-690X"],"issn-type":[{"type":"print","value":"0219-6913"},{"type":"electronic","value":"1793-690X"}],"subject":[],"published":{"date-parts":[[2021,10,6]]},"article-number":"2150044"}}