On the Laplacian in the halfspace with a periodic boundary condition

DOI10.1007/s11512-005-0012-3zbMath1170.35485OpenAlexW2017866979MaRDI QIDQ1005734

Rupert L. Frank

Publication date: 9 March 2009

Published in: Arkiv för Matematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11512-005-0012-3

zbMATH Keywords

scatteringspectrumLaplacianweak \(L_p\)-spaces

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) General topics in linear spectral theory for PDEs (35P05) Scattering theory for PDEs (35P25) General theory of partial differential operators (47F05) Integral operators (47G10)

Related Items (1)

Spectral and scattering properties at thresholds for the Laplacian in a half-space with a periodic boundary condition

Cites Work

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• Scattering theory for systems with different spatial asymptotics on the left and right
• On the scattering theory of the Laplacian with a periodic boundary condition. I. Existence of wave operators
• On the scattering theory of the Laplacian with a periodic boundary condition. II. Additional channels of scattering
• Absolute continuity of the spectrum of a Schrödinger operator with a potential which is periodic in some directions and decays in others
• Absolutely continuous spectrum for the isotropic Maxwell operator with coefficients that are periodic in some directions and decay in others
• Quantum-mechanical scattering by impenetrable periodic surfaces
• On the spectral and wave propagation properties of the surface Maryland model

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