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On the Laplacian in the halfspace with a periodic boundary condition
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2006 (English)In: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 44, no 2, 277-298 p.Article in journal (Refereed) Published
Abstract [en]

We study spectral and scattering properties of the Laplacian H-(sigma)= - Delta in L-2 (R-+(d+1)) corresponding to the boundary condition (partial derivative u)/(partial derivative v) + partial derivative u = 0 with a periodic function sigma. For non-negative sigma we prove that H-(sigma) is unitarily equivalent to the Neumann Laplacian H-(0). In general, there appear additional channels of scattering due to surface states. We prove absolute continuity of the spectrum of H-(sigma) under mild assumptions on sigma.

Place, publisher, year, edition, pages
2006. Vol. 44, no 2, 277-298 p.
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URN: urn:nbn:se:kth:diva-37718DOI: 10.1007/s11512-005-0012-3ISI: 000244917300005ScopusID: 2-s2.0-34147215636OAI: diva2:435105
QC 20110817Available from: 2011-08-17 Created: 2011-08-16 Last updated: 2011-08-17Bibliographically approved

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Frank, Rupert L.
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