{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,20]],"date-time":"2025-09-20T18:26:35Z","timestamp":1758392795237,"version":"3.41.2"},"reference-count":11,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2023,1]]},"abstract":"<jats:p> In this paper, we will present several new results in finite and countable dimensional separable real Hilbert space phase retrieval and norm retrieval by fusion frames. We will characterize of norm retrieval for fusion frames similar norm retrieval for vectors and we will show that only one direction holds for fusion frames. In similar vector case, we will show that every tight fusion frame can do norm retrieval. Also we will show that the unitary operators preserve phase (norm) retrievability of fusion frames. We will make a detailed study of when hyperplanes do norm retrieval and show a general result about it. We will provide numerous examples to show that our results are best possible. <\/jats:p>","DOI":"10.1142\/s0219691322500400","type":"journal-article","created":{"date-parts":[[2022,8,26]],"date-time":"2022-08-26T07:25:31Z","timestamp":1661498731000},"source":"Crossref","is-referenced-by-count":1,"title":["A note on phase (norm) retrievable real Hilbert space fusion frames"],"prefix":"10.1142","volume":"21","author":[{"given":"P. G.","family":"Casazza","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Missouri, Columbia, USA"}]},{"given":"F.","family":"Akrami","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Maragheh, Maragheh, Iran"}]},{"given":"A.","family":"Rahimi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Maragheh, Maragheh, Iran"}]}],"member":"219","published-online":{"date-parts":[[2022,10,13]]},"reference":[{"issue":"2","key":"S0219691322500400BIB001","doi-asserted-by":"crossref","first-page":"126620","DOI":"10.1016\/j.jmaa.2022.126620","volume":"517","author":"Akrami F.","year":"2022","journal-title":"J. Math. Anal. Appl."},{"key":"S0219691322500400BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2005.07.001"},{"key":"S0219691322500400BIB005","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1090\/btran\/12","volume":"3","author":"Cahill J.","year":"2016","journal-title":"Trans. AMS, Series B"},{"issue":"2","key":"S0219691322500400BIB007","first-page":"537","volume":"42","author":"Cahill J.","year":"2016","journal-title":"Houston J. Math."},{"key":"S0219691322500400BIB009","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3390\/axioms6010006","volume":"6","author":"Casazza P. G.","year":"2017","journal-title":"Axioms"},{"key":"S0219691322500400BIB010","series-title":"Contemporary Mathematics","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1090\/conm\/345\/06242","volume-title":"Wavelets, Frames, and Operator Theory","volume":"345","author":"Casazza P. G.","year":"2004"},{"key":"S0219691322500400BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2007.10.001"},{"key":"S0219691322500400BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-8224-8"},{"volume-title":"Principles of Protein X-ray Crystallography","year":"2010","author":"Drenth J.","key":"S0219691322500400BIB014"},{"key":"S0219691322500400BIB015","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1952-0047179-6"},{"key":"S0219691322500400BIB016","doi-asserted-by":"crossref","first-page":"425","DOI":"10.13001\/1081-3810.3260","volume":"31","author":"Hasankhani Fard M. A.","year":"2016","journal-title":"Electron. J. Linear Algebra"}],"container-title":["International Journal of Wavelets, Multiresolution and Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219691322500400","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,7]],"date-time":"2022-12-07T05:05:51Z","timestamp":1670389551000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0219691322500400"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,13]]},"references-count":11,"journal-issue":{"issue":"01","published-print":{"date-parts":[[2023,1]]}},"alternative-id":["10.1142\/S0219691322500400"],"URL":"https:\/\/doi.org\/10.1142\/s0219691322500400","relation":{},"ISSN":["0219-6913","1793-690X"],"issn-type":[{"type":"print","value":"0219-6913"},{"type":"electronic","value":"1793-690X"}],"subject":[],"published":{"date-parts":[[2022,10,13]]},"article-number":"2250040"}}