{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T11:30:29Z","timestamp":1740137429425,"version":"3.37.3"},"reference-count":40,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","funder":[{"DOI":"10.13039\/501100001412","name":"Council of Scientific and Industrial Research, India","doi-asserted-by":"crossref","award":["09\/045(1680)\/2019-EMR-I."],"award-info":[{"award-number":["09\/045(1680)\/2019-EMR-I."]}],"id":[{"id":"10.13039\/501100001412","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2021,3]]},"abstract":"<jats:p> In this paper, we study multivariate Gabor frames in matrix-valued signal spaces over locally compact abelian (LCA) groups, where the lower frame condition depends on a bounded linear operator [Formula: see text] on the underlying matrix-valued signal space. This type of Gabor frame is also known as a multivariate [Formula: see text]-Gabor frame. By extending work of G[Formula: see text]vruta, we present necessary and sufficient conditions for the existence of [Formula: see text]-Gabor frames of multivariate matrix-valued Gabor systems. Some operators which can transform multivariate matrix-valued Gabor and [Formula: see text]-Gabor frames into [Formula: see text]-Gabor frames in terms of adjointable operators are discussed. Finally, we give a Paley\u2013Wiener-type perturbation result for multivariate matrix-valued [Formula: see text]-Gabor frames. <\/jats:p>","DOI":"10.1142\/s0219691320500691","type":"journal-article","created":{"date-parts":[[2020,10,15]],"date-time":"2020-10-15T08:11:10Z","timestamp":1602749470000},"page":"2050069","source":"Crossref","is-referenced-by-count":3,"title":["Multivariate Gabor frames for operators in matrix-valued signal spaces over locally compact abelian groups"],"prefix":"10.1142","volume":"19","author":[{"given":"Divya","family":"Jindal","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Delhi, Delhi 110007, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Uttam Kumar","family":"Sinha","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shivaji College, University of Delhi, New Delhi 110027, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Geetika","family":"Verma","sequence":"additional","affiliation":[{"name":"Centre for Industrial and Applied Mathematics, School of Information Technology and Mathematical Sciences, University of South Australia, Adelaide, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2020,11,30]]},"reference":[{"key":"S0219691320500691BIB001","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1995-1242070-5"},{"key":"S0219691320500691BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2008.06.024"},{"key":"S0219691320500691BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2016.10.027"},{"key":"S0219691320500691BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2015.08.014"},{"issue":"1","key":"S0219691320500691BIB005","first-page":"13","volume":"7","author":"Antol\u00edn A. S.","year":"2012","journal-title":"J. Appl. Funct. Anal."},{"key":"S0219691320500691BIB006","doi-asserted-by":"publisher","DOI":"10.7153\/oam-10-61"},{"volume-title":"Harmonic Analysis and Applications","year":"1997","author":"Benedetto J.","key":"S0219691320500691BIB007"},{"key":"S0219691320500691BIB008","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-8373-3_7"},{"volume-title":"Finite Frames: Theory and Applications","year":"2012","author":"Casazza P. G.","key":"S0219691320500691BIB009"},{"key":"S0219691320500691BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-25613-9"},{"key":"S0219691320500691BIB011","doi-asserted-by":"publisher","DOI":"10.1063\/1.527388"},{"key":"S0219691320500691BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2014.03.010"},{"key":"S0219691320500691BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/j.geomphys.2016.12.019"},{"key":"S0219691320500691BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/s11005-016-0846-6"},{"key":"S0219691320500691BIB015","doi-asserted-by":"publisher","DOI":"10.1007\/s00025-018-0843-4"},{"issue":"3","key":"S0219691320500691BIB016","first-page":"887","volume":"44","author":"Deepshikha","year":"2018","journal-title":"Houston J. Math."},{"key":"S0219691320500691BIB017","doi-asserted-by":"publisher","DOI":"10.1016\/j.geomphys.2018.07.021"},{"key":"S0219691320500691BIB018","doi-asserted-by":"publisher","DOI":"10.1007\/s00025-017-0704-6"},{"key":"S0219691320500691BIB019","doi-asserted-by":"publisher","DOI":"10.1016\/j.geomphys.2011.02.006"},{"key":"S0219691320500691BIB020","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1966-0203464-1"},{"key":"S0219691320500691BIB021","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1952-0047179-6"},{"key":"S0219691320500691BIB022","doi-asserted-by":"publisher","DOI":"10.1006\/acha.1995.1012"},{"key":"S0219691320500691BIB023","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-2016-9"},{"key":"S0219691320500691BIB024","first-page":"163","volume-title":"Proc. SampTA 2001","author":"Feichtinger H. G.","year":"2001"},{"issue":"2","key":"S0219691320500691BIB025","first-page":"273","volume":"48","author":"Frank M.","year":"2002","journal-title":"J. Operator Theory"},{"key":"S0219691320500691BIB026","first-page":"429","volume":"93","author":"Gabor D.","year":"1946","journal-title":"J. Inst. Electr. Eng."},{"key":"S0219691320500691BIB027","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2011.07.006"},{"key":"S0219691320500691BIB028","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2012.08.007"},{"key":"S0219691320500691BIB029","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-68530-4"},{"volume-title":"Functional Analysis","year":"1982","author":"Heuser H. G.","key":"S0219691320500691BIB030"},{"key":"S0219691320500691BIB031","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1007\/s11040-018-9280-6","volume":"21","author":"Jyoti","year":"2018","journal-title":"Math. Phys. Anal. Geom."},{"key":"S0219691320500691BIB032","doi-asserted-by":"publisher","DOI":"10.1142\/S0219691318500224"},{"key":"S0219691320500691BIB033","doi-asserted-by":"publisher","DOI":"10.1007\/s00025-019-1050-7"},{"key":"S0219691320500691BIB034","doi-asserted-by":"publisher","DOI":"10.1007\/s11005-009-0306-7"},{"key":"S0219691320500691BIB035","doi-asserted-by":"publisher","DOI":"10.1142\/S0219691319500553"},{"key":"S0219691320500691BIB036","doi-asserted-by":"publisher","DOI":"10.1016\/j.geomphys.2016.08.009"},{"key":"S0219691320500691BIB037","doi-asserted-by":"publisher","DOI":"10.1216\/RMJ-2018-48-2-661"},{"key":"S0219691320500691BIB038","doi-asserted-by":"publisher","DOI":"10.1007\/s00025-012-0266-6"},{"key":"S0219691320500691BIB039","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-06-08531-5"},{"issue":"1","key":"S0219691320500691BIB040","first-page":"31","volume":"5","author":"Zalik R. A.","year":"2010","journal-title":"J. Appl. Funct. Anal."}],"container-title":["International Journal of Wavelets, Multiresolution and Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219691320500691","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,15]],"date-time":"2021-03-15T08:28:27Z","timestamp":1615796907000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219691320500691"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,30]]},"references-count":40,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2021,3]]}},"alternative-id":["10.1142\/S0219691320500691"],"URL":"https:\/\/doi.org\/10.1142\/s0219691320500691","relation":{},"ISSN":["0219-6913","1793-690X"],"issn-type":[{"type":"print","value":"0219-6913"},{"type":"electronic","value":"1793-690X"}],"subject":[],"published":{"date-parts":[[2020,11,30]]}}}