{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:31:55Z","timestamp":1777447915647,"version":"3.51.4"},"reference-count":16,"publisher":"SAGE Publications","issue":"3-4","license":[{"start":{"date-parts":[[2018,9,14]],"date-time":"2018-09-14T00:00:00Z","timestamp":1536883200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2018,9,14]]},"abstract":"<jats:p>Practical applications of semiclassical measures are tightly connected with a so called oscillatory property, prevailing leakage of information related to high frequencies. In this paper we propose a complementary, concentratory property which prevents loss of information related to low frequencies. We demonstrate that semiclassical measures attain the best performance level if both the properties are satisfied simultaneously, and address a question if this is possible to achieve for an arbitrary bounded [Formula: see text] sequence, providing a negative answer. Comparison of H-measures with semiclassical ones is presented, showing precedence of the latter for problems exhibiting just a single frequency scale. Finally, we present some (strong) compactness results based on the above properties.<\/jats:p>","DOI":"10.3233\/asy-181474","type":"journal-article","created":{"date-parts":[[2018,9,14]],"date-time":"2018-09-14T11:51:44Z","timestamp":1536925904000},"page":"171-192","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Characteristic scales of bounded L2\u00a0sequences"],"prefix":"10.1177","volume":"109","author":[{"given":"Marko","family":"Erceg","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Zagreb, Bijeni\u010dka cesta 30, Zagreb,\u00a0Croatia. E-mail:\u00a0"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Martin","family":"Lazar","sequence":"additional","affiliation":[{"name":"University of Dubrovnik, \u0106ira Cari\u0107a 4, Dubrovnik, Croatia. 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N\n                      \u2218\n                      XVI)\n                      , Ecole Polytechnique, Palaiseau, 1991."},{"key":"ref008","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0312(199704)50:4<323::AID-CPA4>3.0.CO;2-C"},{"key":"ref009","doi-asserted-by":"publisher","DOI":"10.1016\/j.exmath.2010.03.001"},{"key":"ref010","doi-asserted-by":"publisher","DOI":"10.1007\/BF01215225"},{"key":"ref011","first-page":"239","volume":"3","author":"Lazar M.","year":"2012","journal-title":"Dynamics of PDE"},{"key":"ref012","doi-asserted-by":"publisher","DOI":"10.4171\/rmi\/143"},{"key":"ref013","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-009-0217-x"},{"key":"ref014","first-page":"181","volume":"29","author":"\u0160nirel\u2019man A.","year":"1974","journal-title":"Uspekhi Mat. Nauk."},{"key":"ref015","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500020606"},{"key":"ref016","unstructured":"L.\u00a0Tartar, The General Theory of Homogenization: A Personalized Introduction, Springer, 2009."}],"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-181474","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/ASY-181474","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-181474","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:36:15Z","timestamp":1777379775000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-181474"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,9,14]]},"references-count":16,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2018,9,14]]}},"alternative-id":["10.3233\/ASY-181474"],"URL":"https:\/\/doi.org\/10.3233\/asy-181474","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,9,14]]}}}