{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,7,1]],"date-time":"2023-07-01T18:29:11Z","timestamp":1688236151484},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2011,12,3]],"date-time":"2011-12-03T00:00:00Z","timestamp":1322870400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2012,11]]},"DOI":"10.1007\/s10444-011-9222-3","type":"journal-article","created":{"date-parts":[[2011,12,3]],"date-time":"2011-12-03T06:06:15Z","timestamp":1322892375000},"page":"505-520","source":"Crossref","is-referenced-by-count":2,"title":["Dimension invariance of finite frames of translates and Gabor frames"],"prefix":"10.1007","volume":"37","author":[{"given":"Jameson","family":"Cahill","sequence":"first","affiliation":[]},{"given":"Shidong","family":"Li","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2011,12,3]]},"reference":[{"key":"9222_CR1","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1006\/acha.1997.0237","volume":"5","author":"JJ Benedetto","year":"1998","unstructured":"Benedetto, J.J., Li, S.: The theory of multiresolution analysis frames and applications to filter banks. Appl. Comput. Harmon. Anal. 5, 389\u2013427 (1998)","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"9222_CR2","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-8176-8224-8","volume-title":"An Introduction to Frames and Riesz Bases","author":"O Christensen","year":"2003","unstructured":"Christensen, O.: An Introduction to Frames and Riesz Bases. Birkh\u00e4user, Boston (2003)"},{"key":"9222_CR3","volume-title":"Frames for Undergraduates","author":"D Larson","year":"2007","unstructured":"Larson, D., Han, D., Kornelson, K., Weber, E.: Frames for Undergraduates. AMS, Providence (2007)"},{"key":"9222_CR4","doi-asserted-by":"crossref","unstructured":"Daubechies, I.: Ten Lectures on Wavelets, SIAM, Philadelphia (1992)","DOI":"10.1137\/1.9781611970104"},{"key":"9222_CR5","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1090\/S0002-9947-1952-0047179-6","volume":"72","author":"R Duffin","year":"1952","unstructured":"Duffin, R., Schaeffer, A.: A class of nonharmonic Fourier series. Trans. Am. Math. Soc. 72, 341\u2013366 (1952)","journal-title":"Trans. Am. Math. Soc."},{"key":"9222_CR6","volume-title":"Gabor Analysis and Algorithms: Theory and Applications","year":"1997","unstructured":"Feichtinger, H.G., Strohmer, T. (eds.): Gabor Analysis and Algorithms: Theory and Applications. Birkh\u00e4user, Basel (1997)"},{"key":"9222_CR7","volume-title":"Foundations of Time-frequency Analysis","author":"KH Gr\u00f6chenig","year":"2000","unstructured":"Gr\u00f6chenig, K.H.: Foundations of Time-frequency Analysis. Birkh\u00e4user, Boston (2000)"},{"issue":"1","key":"9222_CR8","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.jat.2004.04.012","volume":"129","author":"D Han","year":"2004","unstructured":"Han, D.: Tight frame approximation for multi-frames and super-frames. J. Approx. Theory 129(1), 78\u201393 (2004)","journal-title":"J. Approx. Theory"},{"key":"9222_CR9","volume-title":"Gabor Duality Characterizations, chapter\u00a07. Harmonic Analysis and Applications","author":"E Hayashi","year":"2006","unstructured":"Hayashi, E., Li, S., Sorrells, T.: Gabor Duality Characterizations, chapter\u00a07. Harmonic Analysis and Applications. Birkh\u00e4user, Boston (2006)"},{"key":"9222_CR10","volume-title":"Gabor Analysis and Algorithms: Theory and Applications","author":"AJEM Janssen","year":"1997","unstructured":"Janssen, A.J.E.M.: The duality condition for Weyl-Heisenberg frames. In: Feichtinger, H.G., Strohmer, T. (eds.) Gabor Analysis and Algorithms: Theory and Applications. Birkh\u00e4user, Basel (1997)"},{"key":"9222_CR11","doi-asserted-by":"crossref","unstructured":"Li, S.: A fast and parametric algorithm for discrete Gabor expansions and the role of various dual windows. In: Proc. SPIE\u201995 Orlando, Conference on Wavelet Applications, pp. 935\u2013945 (1995)","DOI":"10.1117\/12.205452"},{"issue":"9&10","key":"9222_CR12","doi-asserted-by":"crossref","first-page":"1181","DOI":"10.1080\/01630569508816668","volume":"16","author":"S Li","year":"1995","unstructured":"Li, S.: On general frame decompositions. Numer. Funct. Anal. Optim. 16(9&10), 1181\u20131191 (1995)","journal-title":"Numer. Funct. Anal. Optim."},{"key":"9222_CR13","doi-asserted-by":"crossref","first-page":"1954","DOI":"10.1109\/18.782117","volume":"45","author":"S Li","year":"1999","unstructured":"Li, S.: Discrete multi-Gabor expansions. IEEE Trans. Inf. 45, 1954\u20131967 (1999)","journal-title":"IEEE Trans. Inf."},{"key":"9222_CR14","doi-asserted-by":"crossref","first-page":"2723","DOI":"10.1155\/S1110865704408178","volume":"17","author":"S Li","year":"2004","unstructured":"Li, S.: Proportional nonuniform multi-Gabor expansions. J. Appl. Signal Proc. 17, 2723\u20132731 (2004)","journal-title":"J. Appl. Signal Proc."},{"issue":"4","key":"9222_CR15","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1007\/s00041-004-3039-0","volume":"10","author":"S Li","year":"2004","unstructured":"Li, S., Ogawa, H.: Pseudoframes for subspaces with applications. J. Fourier Anal. Appl. 10(4), 409\u2013431 (2004)","journal-title":"J. Fourier Anal. Appl."},{"key":"9222_CR16","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/s10440-008-9419-8","volume":"107","author":"S Li","year":"2009","unstructured":"Li, S., Yan, D.: Frame fundamental sensor modeling and stability of one-sided frame perturbation. Acta Appl. Math. 107, 91\u2013103 (2009)","journal-title":"Acta Appl. Math."},{"issue":"5","key":"9222_CR17","doi-asserted-by":"crossref","first-page":"1051","DOI":"10.4153\/CJM-1995-056-1","volume":"47","author":"A Ron","year":"1995","unstructured":"Ron, A., Shen, Z.: Frames and stable bases for shift-invariant subspaces of $L_2(\\mathbb{R}^d)$ . Can. J. Math. 47(5), 1051\u20131094 (1995)","journal-title":"Can. J. Math."},{"issue":"2","key":"9222_CR18","doi-asserted-by":"crossref","first-page":"408","DOI":"10.1006\/jfan.1996.3079","volume":"148","author":"A Ron","year":"1997","unstructured":"Ron, A., Shen, Z.: Affine systems in $L_2(\\mathbb{R}^d)$ : the analysis of the analysis operator. J. Funct. Anal. 148(2), 408\u2013447 (1997)","journal-title":"J. Funct. Anal."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-011-9222-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-011-9222-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-011-9222-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,20]],"date-time":"2019-06-20T06:35:11Z","timestamp":1561012511000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-011-9222-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,12,3]]},"references-count":18,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2012,11]]}},"alternative-id":["9222"],"URL":"https:\/\/doi.org\/10.1007\/s10444-011-9222-3","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,12,3]]}}}