Sharp Weyl Law for Signed Counting Function of Positive Interior Transmission Eigenvalues

DOI10.1137/140966277zbMath1331.35252arXiv1401.6213OpenAlexW2963266935MaRDI QIDQ2943506

Boris Vainberg, Evgeny Lakshtanov

Publication date: 3 September 2015

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.6213

zbMATH Keywords

anisotropic mediainterior transmission eigenvaluesShapiro-Lopatinski condition

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) (Semi-) Fredholm operators; index theories (47A53) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46) Boundary value problems for second-order elliptic systems (35J57)

Related Items (7)

Looking Back on Inverse Scattering Theory ⋮ The Weyl Law of Transmission Eigenvalues and the Completeness of Generalized Transmission Eigenfunctions without Complementing Conditions ⋮ Solvability of interior transmission problem for the diffusion equation by constructing its Green function ⋮ The Weyl law of transmission eigenvalues and the completeness of generalized transmission eigenfunctions ⋮ Boris Rufimovich Vainberg ⋮ Difference Factorizations and Monotonicity in Inverse Medium Scattering for Contrasts with Fixed Sign on the Boundary ⋮ Inside–outside duality with artificial backgrounds

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
• Corners always scatter
• Some inequalities between Dirichlet and Neumann eigenvalues
• An analogue of Weyl's theorem for unbounded domains. I
• Transmission eigenvalues and a problem of Hans Lewy
• Spectral duality for planar billiards
• Discreteness of Transmission Eigenvalues via Upper Triangular Compact Operators
• Ellipticity in the Interior Transmission Problem in Anisotropic Media
• Complex transmission eigenvalues for spherically stratified media
• Weyl Type Bound on Positive Interior Transmission Eigenvalues
• Bounds on positive interior transmission eigenvalues
• The Interior Transmission Problem and Inverse Scattering from Inhomogeneous Media
• THE INVERSE SCATTERING PROBLEM FOR TIME-HARMONIC ACOUSTIC WAVES IN AN INHOMOGENEOUS MEDIUM
• The Denseness of the Far Field Patterns for the Transmission Problem
• Asymptotic behalrior of the scattering phase for exterior domains
• Semiclassical quantization of chaotic billiards: a scattering theory approach
• Asymptotique de la phase de diffusion à haute énergie pour des perturbations du second ordre du laplacien
• Spectral asymmetry and Riemannian geometry. III
• Remarks on interior transmission eigenvalues, Weyl formula and branching billiards
• Spectral analysis of the interior transmission eigenvalue problem
• Completeness of generalized transmission eigenstates
• Applications of elliptic operator theory to the isotropic interior transmission eigenvalue problem
• The inside–outside duality for scattering problems by inhomogeneous media
• The Interior Transmission Problem: Spectral Theory
• Spectral shift function in the large coupling constant limit
• The spectral shift function and the invariance principle

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