Asymptotics of the number of the interior transmission eigenvalues

DOI10.4171/JST/154zbMath1458.35291arXiv1403.3949MaRDI QIDQ528810

Vesselin Petkov, Georgi Vodev

Publication date: 16 May 2017

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

Full work available at URL: https://arxiv.org/abs/1403.3949

zbMATH Keywords

eigenvalue-free regionsinterior transmission eigenvaluesWeyl formula with remainder

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Scattering theory for PDEs (35P25) Asymptotic distributions of eigenvalues in context of PDEs (35P20)

Related Items (18)

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 ⋮ Carleman estimates for elliptic operators with complex coefficients. II: Transmission problems ⋮ 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 ⋮ Sharp Weyl Law for Signed Counting Function of Positive Interior Transmission Eigenvalues ⋮ Asymptotic expansions of transmission eigenvalues for small perturbations of media with generally signed contrast ⋮ Behaviour of large eigenvalues for the asymmetric quantum Rabi model ⋮ The Weyl Law of Transmission Eigenvalues and the Completeness of Generalized Transmission Eigenfunctions without Complementing Conditions ⋮ Improved parametrix in the glancing region for the interior Dirichlet-to-Neumann map ⋮ Localization of the interior transmission eigenvalues for a ball ⋮ Transmission eigenvalue-free regions ⋮ Semiclassical parametrix for the Maxwell equation and applications to the electromagnetic transmission eigenvalues ⋮ The Weyl law of transmission eigenvalues and the completeness of generalized transmission eigenfunctions ⋮ Non-scattering energies for acoustic-type equations on manifolds with a single flat end ⋮ Spectral properties of the inner eigenvalues of transmission ⋮ Weyl formula for the eigenvalues of the dissipative acoustic operator

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