{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T11:30:28Z","timestamp":1740137428344,"version":"3.37.3"},"reference-count":24,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"DOI":"10.13039\/501100003995","name":"Natural Science Foundation of Anhui Province","doi-asserted-by":"publisher","award":["1908085MF175"],"award-info":[{"award-number":["1908085MF175"]}],"id":[{"id":"10.13039\/501100003995","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["JZ2019HGBZ0129"],"award-info":[{"award-number":["JZ2019HGBZ0129"]}],"id":[{"id":"10.13039\/501100012226","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":[[2020,7]]},"abstract":"<jats:p> In this paper, we prove that the unconditional constants of the g-frame expansion in a Hilbert space are bounded by [Formula: see text], where [Formula: see text], [Formula: see text] are the frame bounds of the g-frames. It follows that tight g-frames have unconditional constant one. Then we generalize this to a classification of such g-frames by showing that a g-Bessel sequence has unconditional constant one if it is an orthogonal sum of g-tight frames. We also obtain a new result under which a g-Bessel sequence is a g-frame from the view of unconditional constant. Finally, we prove similar results for cross g-frame expansions as long as the cross g-frame expansions stay uniformly bounded away from zero. <\/jats:p>","DOI":"10.1142\/s0219691320500228","type":"journal-article","created":{"date-parts":[[2020,2,4]],"date-time":"2020-02-04T07:37:19Z","timestamp":1580801839000},"page":"2050022","source":"Crossref","is-referenced-by-count":1,"title":["Unconditional convergence constants of g-frame expansions"],"prefix":"10.1142","volume":"18","author":[{"given":"Dongwei","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematics, Hefei University of Technology, Hefei, Anhui 230009, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2020,3,3]]},"reference":[{"key":"S0219691320500228BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2016.12.013"},{"key":"S0219691320500228BIB002","first-page":"445","volume":"2","author":"Benedetto J. J.","year":"1992","journal-title":"Wavelets, Tutor. Theory Appl."},{"key":"S0219691320500228BIB003","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/345\/06242"},{"key":"S0219691320500228BIB004","doi-asserted-by":"publisher","DOI":"10.1109\/SAMPTA.2015.7148913"},{"key":"S0219691320500228BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2003.12.003"},{"key":"S0219691320500228BIB006","doi-asserted-by":"publisher","DOI":"10.1109\/18.57199"},{"key":"S0219691320500228BIB007","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970104"},{"key":"S0219691320500228BIB008","doi-asserted-by":"publisher","DOI":"10.1063\/1.527388"},{"key":"S0219691320500228BIB009","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1952-0047179-6"},{"key":"S0219691320500228BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/s00041-011-9182-5"},{"key":"S0219691320500228BIB011","doi-asserted-by":"publisher","DOI":"10.1109\/18.985949"},{"key":"S0219691320500228BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2003.09.041"},{"key":"S0219691320500228BIB013","doi-asserted-by":"publisher","DOI":"10.1006\/acha.2000.0340"},{"key":"S0219691320500228BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2016.04.002"},{"key":"S0219691320500228BIB015","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2014.2320937"},{"key":"S0219691320500228BIB016","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-4687-5"},{"key":"S0219691320500228BIB017","doi-asserted-by":"publisher","DOI":"10.1007\/s00025-016-0587-y"},{"key":"S0219691320500228BIB018","doi-asserted-by":"publisher","DOI":"10.1142\/S0219691318500534"},{"key":"S0219691320500228BIB019","doi-asserted-by":"publisher","DOI":"10.1016\/j.dsp.2017.10.002"},{"key":"S0219691320500228BIB020","doi-asserted-by":"publisher","DOI":"10.1007\/s00041-004-3039-0"},{"issue":"3","key":"S0219691320500228BIB021","first-page":"271","volume":"14","author":"Najati A.","year":"2008","journal-title":"Methods Funct. Anal. Topology"},{"key":"S0219691320500228BIB022","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2005.09.039"},{"key":"S0219691320500228BIB023","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2006.03.043"},{"key":"S0219691320500228BIB024","doi-asserted-by":"publisher","DOI":"10.1007\/s00041-016-9501-y"}],"container-title":["International Journal of Wavelets, Multiresolution and Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219691320500228","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,12]],"date-time":"2020-08-12T13:57:22Z","timestamp":1597240642000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219691320500228"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,3]]},"references-count":24,"journal-issue":{"issue":"04","published-print":{"date-parts":[[2020,7]]}},"alternative-id":["10.1142\/S0219691320500228"],"URL":"https:\/\/doi.org\/10.1142\/s0219691320500228","relation":{},"ISSN":["0219-6913","1793-690X"],"issn-type":[{"type":"print","value":"0219-6913"},{"type":"electronic","value":"1793-690X"}],"subject":[],"published":{"date-parts":[[2020,3,3]]}}}