{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:48:17Z","timestamp":1777448897480,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"1-2","license":[{"start":{"date-parts":[[2011,7,1]],"date-time":"2011-07-01T00:00:00Z","timestamp":1309478400000},"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":[[2011,7]]},"abstract":"<jats:p>\n                    We analyze a general class of difference operators H\n                    <jats:sub>\u03b5<\/jats:sub>\n                    =T\n                    <jats:sub>\u03b5<\/jats:sub>\n                    +V\n                    <jats:sub>\u03b5<\/jats:sub>\n                    on \u2113\n                    <jats:sup>2<\/jats:sup>\n                    ((\u03b5Z)\n                    <jats:sup>d<\/jats:sup>\n                    ), where V\n                    <jats:sub>\u03b5<\/jats:sub>\n                    is a one-well potential and \u03b5 is a small parameter. We construct formal asymptotic expansions of WKB-type for eigenfunctions associated with the low lying eigenvalues of H\n                    <jats:sub>\u03b5<\/jats:sub>\n                    . These are obtained from eigenfunctions or quasimodes for the operator H\n                    <jats:sub>\u03b5<\/jats:sub>\n                    , acting on L\n                    <jats:sup>2<\/jats:sup>\n                    (R\n                    <jats:sup>d<\/jats:sup>\n                    ), via restriction to the lattice (\u03b5Z)\n                    <jats:sup>d<\/jats:sup>\n                    .\n                  <\/jats:p>","DOI":"10.3233\/asy-2010-1025","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:16:43Z","timestamp":1575055003000},"page":"1-36","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":6,"title":["Asymptotic eigenfunctions for a class of difference operators"],"prefix":"10.1177","volume":"73","author":[{"given":"Markus","family":"Klein","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Mathematik, Universit\u00e4t Potsdam, Am Neuen Palais 10, 14469 Potsdam, Germany. E-mails: mklein@math.uni-potsdam.de; erosen@uni-potsdam.de"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Elke","family":"Rosenberger","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Mathematik, Universit\u00e4t Potsdam, Am Neuen Palais 10, 14469 Potsdam, Germany. E-mails: mklein@math.uni-potsdam.de; erosen@uni-potsdam.de"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2011,7,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2010-1025","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2010-1025","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:39:19Z","timestamp":1777379959000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-2010-1025"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,7]]},"references-count":0,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2011,7]]}},"alternative-id":["10.3233\/ASY-2010-1025"],"URL":"https:\/\/doi.org\/10.3233\/asy-2010-1025","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,7]]}}}