{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:48:46Z","timestamp":1777448926807,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2012,1,1]],"date-time":"2012-01-01T00:00:00Z","timestamp":1325376000000},"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":[[2012,1]]},"abstract":"<jats:p>The Laplacian in an unbounded tubular neighbourhood of a hyperplane with non-Hermitian complex-symmetric Robin-type boundary conditions is investigated in the limit when the width of the neighbourhood diminishes. We show that the Laplacian converges in a norm resolvent sense to a self-adjoint Schr\u00f6dinger operator in the hyperplane whose potential is expressed solely in terms of the boundary coupling function. As a consequence, we are able to explain some peculiar spectral properties of the non-Hermitian Laplacian by known results for Schr\u00f6dinger operators.<\/jats:p>","DOI":"10.3233\/asy-2011-1061","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:19:30Z","timestamp":1575055170000},"page":"49-59","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":11,"title":["The effective Hamiltonian for thin layers with non-Hermitian Robin-type boundary conditions"],"prefix":"10.1177","volume":"76","author":[{"given":"Denis","family":"Borisov","sequence":"first","affiliation":[{"name":"Bashkir State Pedagogical University, October St. 3a, 450000 Ufa, Russian Federation. E-mail: borisovdi@yandex.ru"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David","family":"Krej\u010di\u0159\u00edk","sequence":"additional","affiliation":[{"name":"Department of Theoretical Physics, Nuclear Physics Institute ASCR, 25068 \u0158e\u017e, Czech Republic. E-mail: krejcirik@ujf.cas.cz"},{"name":"IKERBASQUE, Basque Foundation for Science, Alameda Urquijo, 36, 5, 48011 Bilbao, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2012,1,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2011-1061","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2011-1061","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:39:26Z","timestamp":1777379966000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-2011-1061"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.3233\/ASY-2011-1061"],"URL":"https:\/\/doi.org\/10.3233\/asy-2011-1061","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,1]]}}}