{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T13:06:37Z","timestamp":1773407197458,"version":"3.50.1"},"reference-count":28,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","funder":[{"name":"Department of Science and Technology, India","award":["DST\/WISE-PDF\/PM-6\/2023"],"award-info":[{"award-number":["DST\/WISE-PDF\/PM-6\/2023"]}]},{"DOI":"10.13039\/501100007063","name":"University of Delhi","doi-asserted-by":"crossref","award":["Ref. No.\/IoE\/2023-24\/12\/FRP"],"award-info":[{"award-number":["Ref. No.\/IoE\/2023-24\/12\/FRP"]}],"id":[{"id":"10.13039\/501100007063","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":[[2024,9]]},"abstract":"<jats:p> A Riesz basis for a separable Hilbert space [Formula: see text] is the image of an orthonormal basis under a bounded, linear and bijective operator acting on [Formula: see text]. Equivalently, it is an exact frame that shares the properties of a basis for [Formula: see text]. Let [Formula: see text] be a [Formula: see text]-compact and metrizable locally compact abelian group, and [Formula: see text] and [Formula: see text] be positive integers. It is illustrated that the image of a matrix-valued orthonormal basis under a bijective, bounded and linear operator acting on the matrix-valued signal space [Formula: see text] may not be a frame, hence not a basis of the space [Formula: see text]. We introduce a notion of matrix-valued Riesz basis in the space [Formula: see text], where the adjointability of a bounded linear operator in the definition of Riesz basis with respect to the matrix-valued inner product plays a crucial role. We establish the existence of matrix-valued Riesz bases of the space [Formula: see text]. Extending results for standard Riesz bases of separable Hilbert spaces, we give necessary and sufficient conditions, and a characterization of matrix-valued Riesz bases of the space [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s021969132450019x","type":"journal-article","created":{"date-parts":[[2024,4,24]],"date-time":"2024-04-24T11:34:23Z","timestamp":1713958463000},"source":"Crossref","is-referenced-by-count":4,"title":["On matrix-valued Riesz bases over LCA groups"],"prefix":"10.1142","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-8736-783X","authenticated-orcid":false,"family":"Jyoti","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Delhi, Delhi 110007, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8634-6920","authenticated-orcid":false,"given":"Lalit Kumar","family":"Vashisht","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Delhi, Delhi 110007, India"}]}],"member":"219","published-online":{"date-parts":[[2024,5,29]]},"reference":[{"key":"S021969132450019XBIB001","doi-asserted-by":"publisher","DOI":"10.1109\/MEMB.2009.934244"},{"issue":"1","key":"S021969132450019XBIB002","first-page":"13","volume":"7","author":"Antol\u00edn A. 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