Transmission eigenvalue-free regions

DOI10.1007/s00220-015-2311-2zbMath1323.35110arXiv1401.1627OpenAlexW1987371078MaRDI QIDQ2018317

Georgi Vodev

Publication date: 14 April 2015

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.1627

zbMATH Keywords

interior transmission problemtransmission eigenvalueeigenvalue-free region

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Inverse problems for PDEs (35R30)

Related Items (21)

Location and Weyl Formula for the Eigenvalues of Some Non Self-Adjoint Operators ⋮ The spectral analysis of the interior transmission eigenvalue problem for Maxwell's equations ⋮ Transmission eigenvalues for strictly concave domains ⋮ Location of eigenvalues for the wave equation with dissipative boundary conditions ⋮ High-frequency approximation of the interior Dirichlet-to-Neumann map and applications to the transmission eigenvalues ⋮ Asymptotic of the dissipative eigenvalues of Maxwell’s equations ⋮ Weyl formula for the negative dissipative eigenvalues of Maxwell's equations ⋮ The Weyl Law of Transmission Eigenvalues and the Completeness of Generalized Transmission Eigenfunctions without Complementing Conditions ⋮ On the distribution of Born transmission eigenvalues in the complex plane ⋮ Approximation of the elastic Dirichlet-to-Neumann map ⋮ Improved parametrix in the glancing region for the interior Dirichlet-to-Neumann map ⋮ The method of fundamental solutions for computing acoustic interior transmission eigenvalues ⋮ On the Discreteness of Transmission Eigenvalues for the Maxwell Equations ⋮ A note on transmission eigenvalues in electromagnetic scattering theory ⋮ Localization of the interior transmission eigenvalues for a ball ⋮ Semiclassical parametrix for the Maxwell equation and applications to the electromagnetic transmission eigenvalues ⋮ Analysis of the linear sampling method for imaging penetrable obstacles in the time domain ⋮ The Weyl law of transmission eigenvalues and the completeness of generalized transmission eigenfunctions ⋮ Eigenvalues for Maxwell’s equations with dissipative boundary conditions ⋮ Weyl formula for the eigenvalues of the dissipative acoustic operator ⋮ The completeness of the generalized eigenfunctions and an upper bound for the counting function of the transmission eigenvalue problem for Maxwell equations

Cites Work

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• Weyl asymptotics of the transmission eigenvalues for a constant index of refraction
• Asymptotics of the number of the interior transmission eigenvalues
• Asymptotics of the number of Rayleigh resonances
• Distribution of resonances for the Neumann problem in linear elasticity outside a strictly convex body
• Neumann resonances in linear elasticity for an arbitrary body
• The interior transmission problem and bounds on transmission eigenvalues
• Weyl Type Bound on Positive Interior Transmission Eigenvalues
• Bounds on positive interior transmission eigenvalues
• Remarks on interior transmission eigenvalues, Weyl formula and branching billiards
• Spectral analysis of the interior transmission eigenvalue problem
• Applications of elliptic operator theory to the isotropic interior transmission eigenvalue problem
• Transmission eigenvalues in one dimension

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