Limiting absorption principle, generalized eigenfunctions, and scattering matrix for Laplace operators with boundary conditions on hypersurfaces

DOI10.4171/JST/231zbMath1402.35194arXiv1605.03240WikidataQ129056162 ScholiaQ129056162MaRDI QIDQ1624166

Andrea Posilicano, Mourad Sini, Andrea Mantile

Publication date: 15 November 2018

Published in: Journal of Spectral Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.03240

zbMATH Keywords

boundary conditionsscattering matrixlimiting absorption principleselfadjoint extensions

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Scattering theory for PDEs (35P25) Second-order elliptic equations (35J15)

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Cites Work

• Self-adjoint elliptic operators with boundary conditions on not closed hypersurfaces
• Spectral estimates for resolvent differences of self-adjoint elliptic operators
• Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
• Schrödinger operators with singular interactions
• Low energy scattering with a penetrable wall interaction
• Spectral and scattering theory for the Schrödinger operators with penetrable wall potentials
• Spectral duality for planar billiards
• Schrödinger operators with \(\delta\) and \(\delta^{\prime}\)-potentials supported on hypersurfaces
• Scattering matrices and Dirichlet-to-Neumann maps
• Eigenfunction expansions associated with the Schrödinger operators and their applications to scattering theory
• On the representation of the potential scattering operator in quantum mechanics
• Spectral and scattering theory for Schrödinger operators
• Generalized interactions supported on hypersurfaces
• Scattering matrices and Weyl functions
• Finite Rank Perturbations, Scattering Matrices and Inverse Problems
• The limiting absorption principle for partial differential operators
• On general boundary problems for elliptic differential equations
• A Krein-like formula for singular perturbations of self-adjoint operators and applications
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