{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T19:34:04Z","timestamp":1773776044589,"version":"3.50.1"},"reference-count":0,"publisher":"European Mathematical Society - EMS - Publishing House GmbH","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Publ. Res. Inst. Math. Sci."],"published-print":{"date-parts":[[2005,9,30]]},"abstract":"<jats:p>The spectrum of the Laplace operator in a curved strip of constant width built along an in\ufb01nite plane curve, subject to three di\ufb00erent types of boundary conditions (Dirichlet, Neumann and a combination of these ones, respectively), is investigated. We prove that the essential spectrum as a set is stable under any curvature of the reference curve which vanishes at in\ufb01nity and \ufb01nd various su\ufb03cient conditions which guarantee the existence of geometrically induced discrete spectrum. Furthermore, we derive a lower bound to the distance between the essential spectrum and the spectral threshold for locally curved strips. The paper is also intended as an overview of some new and old results on spectral properties of curved quantum waveguides.<\/jats:p>","DOI":"10.2977\/prims\/1145475229","type":"journal-article","created":{"date-parts":[[2006,9,13]],"date-time":"2006-09-13T11:37:00Z","timestamp":1158147420000},"page":"757-791","source":"Crossref","is-referenced-by-count":56,"title":["On the Spectrum of Curved Planar Waveguides"],"prefix":"10.4171","volume":"41","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2442-1331","authenticated-orcid":false,"given":"David","family":"Krej\u010di\u0159\u00edk","sequence":"first","affiliation":[{"name":"Czech Technical University in Prague, Czech Republic"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8089-6729","authenticated-orcid":false,"given":"Jan","family":"K\u0159\u00ed\u017e","sequence":"additional","affiliation":[{"name":"University Hradec Kr\u00e1lov\u00e9, Hradec Kralove, Czech Republic"}]}],"member":"2673","container-title":["Publications of the Research Institute for Mathematical Sciences"],"original-title":[],"link":[{"URL":"http:\/\/www.ems-ph.org\/fulltext\/10.2977\/prims\/1145475229","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T13:43:59Z","timestamp":1762955039000},"score":1,"resource":{"primary":{"URL":"https:\/\/ems.press\/doi\/10.2977\/prims\/1145475229"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,9,30]]},"references-count":0,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.2977\/prims\/1145475229","relation":{},"ISSN":["0034-5318","1663-4926"],"issn-type":[{"value":"0034-5318","type":"print"},{"value":"1663-4926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,9,30]]}}}