Discreteness of Transmission Eigenvalues via Upper Triangular Compact Operators
From MaRDI portal
Publication:2882320
DOI10.1137/110836420zbMath1238.81172arXiv1104.4336OpenAlexW2041390660MaRDI QIDQ2882320
Publication date: 4 May 2012
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1104.4336
inverse problemsHelmholtz equationinverse scatteringtransmission eigenvaluesupper triangular compact
Scattering theory for PDEs (35P25) Diffraction, scattering (78A45) Inverse scattering problems in quantum theory (81U40)
Related Items (37)
On local and global structures of transmission eigenfunctions and beyond ⋮ The spectral analysis of the interior transmission eigenvalue problem for Maxwell's equations ⋮ Transmission eigenvalue problem for inhomogeneous absorbing media with mixed boundary condition ⋮ Limiting absorption principle and well-posedness for the Helmholtz equation with sign changing coefficients ⋮ Mathematics of Hybrid Imaging: A Brief Review ⋮ Bilaplacian problems with a sign-changing coefficient ⋮ Weyl Type Bound on Positive Interior Transmission Eigenvalues ⋮ Interface with weakly singular points always scatter ⋮ Sampling methods for reconstructing the geometry of a local perturbation in unknown periodic layers ⋮ The generalized linear sampling and factorization methods only depends on the sign of contrast on the boundary ⋮ Sharp Weyl Law for Signed Counting Function of Positive Interior Transmission Eigenvalues ⋮ Surface integral formulation of the interior transmission problem ⋮ Asymptotic expansions of transmission eigenvalues for small perturbations of media with generally signed contrast ⋮ On vanishing and localizing of transmission eigenfunctions near singular points: a numerical study ⋮ The Weyl Law of Transmission Eigenvalues and the Completeness of Generalized Transmission Eigenfunctions without Complementing Conditions ⋮ A note on Sylvester's proof of discreteness of interior transmission eigenvalues ⋮ A boundary integral equation method for the transmission eigenvalue problem ⋮ Counting function for interior transmission eigenvalues ⋮ Boundary integral equations for the transmission eigenvalue problem for Maxwell's equations ⋮ Weyl asymptotics of the transmission eigenvalues for a constant index of refraction ⋮ Rellich type theorems for unbounded domains ⋮ On the Discreteness of Transmission Eigenvalues for the Maxwell Equations ⋮ Acoustic scattering from corners, edges and circular cones ⋮ New interior transmission problem applied to a single Floquet–Bloch mode imaging of local perturbations in periodic media ⋮ A duality between scattering poles and transmission eigenvalues in scattering theory ⋮ Discreteness of interior transmission eigenvalues revisited ⋮ Discreteness of Transmission Eigenvalues for Higher-Order Main Terms and Perturbations ⋮ Solvability of interior transmission problem for the diffusion equation by constructing its Green function ⋮ The Generalized Linear Sampling Method for Limited Aperture Measurements ⋮ The Weyl law of transmission eigenvalues and the completeness of generalized transmission eigenfunctions ⋮ Electromagnetic interior transmission eigenvalue problem for an inhomogeneous medium with a conductive boundary ⋮ Spectral properties of the inner eigenvalues of transmission ⋮ The completeness of the generalized eigenfunctions and an upper bound for the counting function of the transmission eigenvalue problem for Maxwell equations ⋮ A perturbation problem for transmission eigenvalues ⋮ Uniqueness in determining refractive indices by formally determined far-field data ⋮ Surface-Localized Transmission Eigenstates, Super-resolution Imaging, and Pseudo Surface Plasmon Modes ⋮ Identifying defects in an unknown background using differential measurements
This page was built for publication: Discreteness of Transmission Eigenvalues via Upper Triangular Compact Operators