{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:45:49Z","timestamp":1777448749622,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"1-2","license":[{"start":{"date-parts":[[2009,4,1]],"date-time":"2009-04-01T00:00:00Z","timestamp":1238544000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2009,4]]},"abstract":"<jats:p>A two-scale Fourier transform for periodic homogenization in Fourier space is introduced. The transform connects the various existing techniques for periodic homogenization, i.e., two-scale convergence, periodic unfolding and the Floquet\u2013Bloch expansion approach to homogenization. It turns out that the two-scale compactness results are easily obtained by the use of the two-scale Fourier transform. Moreover, the Floquet\u2013Bloch eigenvalue problems for differential operators is recovered in a natural and straight forward way by the use of this transform. The transform is generalized to the (N+1)-scale case.<\/jats:p>","DOI":"10.3233\/asy-2008-0914","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:04:47Z","timestamp":1575054287000},"page":"1-40","source":"Crossref","is-referenced-by-count":7,"title":["The two-scale Fourier transform approach to homogenization; periodic homogenization in Fourier space"],"prefix":"10.1177","volume":"62","author":[{"given":"Niklas","family":"Wellander","sequence":"first","affiliation":[{"name":"Swedish Defence Research Agency, FOI, SE-581 11 Link\u00f6ping, Sweden"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2009,4,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2008-0914","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2008-0914","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:38:49Z","timestamp":1777379929000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-2008-0914"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,4]]},"references-count":0,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2009,4]]}},"alternative-id":["10.3233\/ASY-2008-0914"],"URL":"https:\/\/doi.org\/10.3233\/asy-2008-0914","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,4]]}}}