{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T19:26:35Z","timestamp":1767986795586,"version":"3.49.0"},"reference-count":26,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"name":"Council for Scientific and Industrial Research, India","award":["09\/045(1680)\/2019-EMR-I"],"award-info":[{"award-number":["09\/045(1680)\/2019-EMR-I"]}]},{"DOI":"10.13039\/501100007063","name":"University of Delhi","doi-asserted-by":"publisher","award":["Ref. No.\/IoE\/2021\/12\/FRP"],"award-info":[{"award-number":["Ref. No.\/IoE\/2021\/12\/FRP"]}],"id":[{"id":"10.13039\/501100007063","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":[[2023,11]]},"abstract":"<jats:p> We study nonstationary frames of matrix-valued Gabor systems and wavelet systems in the matrix-valued function space [Formula: see text]. First, we show that a diagonal matrix-valued window function constitutes a frame for [Formula: see text] whenever each diagonal entry constitutes a frame for the space [Formula: see text]. This is not true for arbitrary nonzero matrix-valued function. Using this, we prove the existence of nonstationary matrix-valued Gabor frames associated with the Weyl\u2013Heisenberg group in terms of density of real numbers. We give a representation of the frame operator of matrix-valued nonstationary Gabor system. A necessary condition with explicit frame bounds for nonstationary matrix-valued Gabor frames associated with the Weyl\u2013Heisenberg group is given. We discuss matrix-valued frame preserving maps in terms of adjointablity, with respect to the matrix-valued inner product, of bounded linear operators acting on [Formula: see text]. It is shown that the image of a matrix-valued Gabor frame under bounded, linear and invertible operator on [Formula: see text] may not be a frame for [Formula: see text]. In this direction, we give sufficient conditions on bounded linear operators which can preserve frame conditions. Finally, we give necessary and sufficient condition for the existence of nonstationary matrix-valued wavelet frames associated with the extended affine group. <\/jats:p>","DOI":"10.1142\/s0219691323500224","type":"journal-article","created":{"date-parts":[[2023,4,13]],"date-time":"2023-04-13T16:14:41Z","timestamp":1681402481000},"source":"Crossref","is-referenced-by-count":7,"title":["Matrix-valued nonstationary frames associated with the Weyl\u2013Heisenberg group and the extended affine group"],"prefix":"10.1142","volume":"21","author":[{"given":"Divya","family":"Jindal","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Delhi, Delhi 110007, India"}]},{"family":"Jyoti","sequence":"additional","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":[[2023,5,10]]},"reference":[{"issue":"6","key":"S0219691323500224BIB002","doi-asserted-by":"crossref","first-page":"1661","DOI":"10.1090\/S0002-9939-1995-1242070-5","volume":"123","author":"Aldroubi A.","year":"1995","journal-title":"Proc. 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