{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,14]],"date-time":"2026-02-14T02:40:14Z","timestamp":1771036814732,"version":"3.50.1"},"reference-count":11,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Stoch. Dyn."],"published-print":{"date-parts":[[2015,9]]},"abstract":"<jats:p> We characterize completely the notion of an exponential dichotomy in average in terms of an admissibility property. The notion corresponds to a generalization of that of an exponential dichotomy to measurable cocycles acting on L<jats:sup>1<\/jats:sup> functions with respect to a given probability measure. The admissibility property is described in terms of the injectivity and surjectivity of a certain linear operator in the space of bounded sequences of L<jats:sup>1<\/jats:sup> functions. The characterization is then used to establish in a simple manner the robustness of the notion, in the sense that it persists under sufficiently small linear perturbations. We note that we consider both \u2124-cocycles and \u2115-cocycles. <\/jats:p>","DOI":"10.1142\/s0219493715500148","type":"journal-article","created":{"date-parts":[[2014,10,29]],"date-time":"2014-10-29T02:48:35Z","timestamp":1414550915000},"page":"1550014","source":"Crossref","is-referenced-by-count":6,"title":["Admissibility for exponential dichotomies in average"],"prefix":"10.1142","volume":"15","author":[{"given":"Luis","family":"Barreira","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal"}]},{"given":"Davor","family":"Dragi\u010devi\u0107","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Rijeka, 51000 Rijeka, Croatia"}]},{"given":"Claudia","family":"Valls","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2015,5,22]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107326026"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.1995.1117"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(67)90014-9"},{"key":"rf4","series-title":"Translations of Mathematical Monographs","volume-title":"Stability of Solutions of Differential Equations in Banach Space","volume":"43","author":"Dalec'ki\u012d Ju.","year":"1974"},{"key":"rf5","series-title":"Mathematical Surveys and Monographs","volume-title":"Asymptotic Behavior of Dissipative Systems","volume":"25","author":"Hale J.","year":"1988"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.2307\/1969871"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/S0362-546X(97)00423-9"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/BF01194662"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1023\/A:1021913903923"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2005.04.011"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-5037-9"}],"container-title":["Stochastics and Dynamics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219493715500148","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T17:57:39Z","timestamp":1565200659000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219493715500148"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,5,22]]},"references-count":11,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2015,5,22]]},"published-print":{"date-parts":[[2015,9]]}},"alternative-id":["10.1142\/S0219493715500148"],"URL":"https:\/\/doi.org\/10.1142\/s0219493715500148","relation":{},"ISSN":["0219-4937","1793-6799"],"issn-type":[{"value":"0219-4937","type":"print"},{"value":"1793-6799","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,5,22]]}}}