{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T11:14:33Z","timestamp":1772450073176,"version":"3.50.1"},"reference-count":13,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p> This paper develops several aspects of shift-invariant spaces on locally compact abelian groups. For a second countable locally compact abelian group G we prove a useful Hilbert space isomorphism, introduce range functions and give a characterization of shift-invariant subspaces of L<jats:sup>2<\/jats:sup>(G) in terms of range functions. Utilizing these functions, we generalize characterizations of frames and Riesz bases generated by shifts of a countable set of generators from L<jats:sup>2<\/jats:sup>(\u211d<jats:sup>n<\/jats:sup>) to L<jats:sup>2<\/jats:sup>(G). <\/jats:p>","DOI":"10.1142\/s0219691310003365","type":"journal-article","created":{"date-parts":[[2010,2,25]],"date-time":"2010-02-25T02:14:11Z","timestamp":1267064051000},"page":"49-59","source":"Crossref","is-referenced-by-count":14,"title":["A RANGE FUNCTION APPROACH TO SHIFT-INVARIANT SPACES ON LOCALLY COMPACT ABELIAN GROUPS"],"prefix":"10.1142","volume":"08","author":[{"given":"R. A.","family":"KAMYABI GOL","sequence":"first","affiliation":[{"name":"Department of Mathematics, Ferdowsi University, P. O. Box 1159, Mashhad 91775, Iran"}]},{"given":"R.","family":"RAISI TOUSI","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Ferdowsi University, P. O. Box 1159, Mashhad 91775, Iran"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1258-4"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1006\/jfan.1994.1003"},{"key":"rf3","first-page":"1","volume":"176","author":"Bownik M.","journal-title":"J. Funct. Anal."},{"key":"rf4","first-page":"387","volume":"51","author":"Bownik M.","journal-title":"Michigan Math. J."},{"key":"rf5","volume-title":"Von Neumann Algebras","author":"Dixmier J.","year":"1981"},{"key":"rf6","volume-title":"A Course in Abstract Harmonic Analysis","author":"Folland G. B.","year":"1995"},{"key":"rf7","series-title":"Springer Lecture Notes in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/b104912","volume-title":"Abstract Harmonic Analysis of Continuous Wavelet Transform","author":"F\u00fchr H.","year":"2005"},{"key":"rf8","volume-title":"Lectures on Invariant Subspaces","author":"Helson H.","year":"1964"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-00102-8"},{"key":"rf10","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/j.jmaa.2007.08.039","volume":"340","author":"Gol R. A. Kamyabi","journal-title":"J. Math. Anal. Appl."},{"key":"rf12","volume-title":"C*-Algebras and Operator Theory","author":"Murphy G. J.","year":"1990"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1006\/jfan.1996.3079"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1995-056-1"}],"container-title":["International Journal of Wavelets, Multiresolution and Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219691310003365","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T17:32:55Z","timestamp":1565199175000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219691310003365"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":13,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1142\/S0219691310003365"],"URL":"https:\/\/doi.org\/10.1142\/s0219691310003365","relation":{},"ISSN":["0219-6913","1793-690X"],"issn-type":[{"value":"0219-6913","type":"print"},{"value":"1793-690X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}