{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:51:42Z","timestamp":1777449102721,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"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":[[2014,1]]},"abstract":"<jats:p>\n                    We determine the range of the incoming wave operator for the pair of operators (\u2212\u0394,\u2212\u0394+V\n                    <jats:sub>1<\/jats:sub>\n                    (x)\u2212i\u03b5V\n                    <jats:sub>2<\/jats:sub>\n                    (x)) on L\n                    <jats:sup>2<\/jats:sup>\n                    (R\n                    <jats:sup>n<\/jats:sup>\n                    ) under the conditions n\u22653 and 0 is a regular point of \u2212\u0394+V\n                    <jats:sub>1<\/jats:sub>\n                    , V\n                    <jats:sub>2<\/jats:sub>\n                    \u22650 and \u03b5&gt;0 is small enough. This implies that the dissipative scattering operator is bijective.\n                  <\/jats:p>","DOI":"10.3233\/asy-131190","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:31:03Z","timestamp":1575055863000},"page":"49-57","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["On the wave operator for dissipative potentials with small imaginary part"],"prefix":"10.1177","volume":"86","author":[{"given":"Xue Ping","family":"Wang","sequence":"first","affiliation":[{"name":"Laboratoire de Math\u00e9matiques Jean Leray, UMR 6629 CNRS, Universit\u00e9 de Nantes, 44322 Nantes Cedex 3, France. E-mails: {xue-ping.wang, lu.zhu}@univ-nantes.fr"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lu","family":"Zhu","sequence":"additional","affiliation":[{"name":"Laboratoire de Math\u00e9matiques Jean Leray, UMR 6629 CNRS, Universit\u00e9 de Nantes, 44322 Nantes Cedex 3, France. E-mails: {xue-ping.wang, lu.zhu}@univ-nantes.fr"},{"name":"Department of Mathematics & IMS, Nanjing University, 210093 Nanjing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2014,1,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-131190","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-131190","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:40:03Z","timestamp":1777380003000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-131190"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2014,1]]}},"alternative-id":["10.3233\/ASY-131190"],"URL":"https:\/\/doi.org\/10.3233\/asy-131190","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1]]}}}