Related papers: Sharp Weyl Law for Signed Counting Function of Pos…
In this paper, we consider an interior transmission eigenvalue (ITE) problem on some compact $C^{\infty }$-Riemannian manifolds with a common smooth boundary. In particular, these manifolds may have different topologies, but we impose some…
The transmission eigenvalue problem is a type of non-elliptic and non-selfadjoint spectral problem that arises in the wave scattering theory when invisibility/transparency occurs. The transmission eigenfunctions are the interior resonant…
This paper contains a lower bound of the Weyl type on the counting function of the positive eigenvalues of the interior transmission eigenvalue problem which justifies the existence of an infinite set of positive interior transmission…
The interior transmission eigenvalue problem (ITP) plays a central role in inverse scattering theory and in the spectral analysis of inhomogeneous media. Despite its smooth dependence on the refractive index at the PDE level, the…
A recent problem of interest in inverse problems has been the study of eigenvalue problems arising from scattering theory and their potential use as target signatures in nondestructive testing of materials. Towards this pursuit we introduce…
The inverse electromagnetic scattering problem for anisotropic media in general does not have a unique solution. A possible approach to this problem is through the use of appropriate "target signatures," i.e. eigenvalues associated with the…
The (interior) transmission eigenvalue problems are a type of non-elliptic, non-selfadjoint and nonlinear spectral problems that arise in the theory of wave scattering. They connect to the direct and inverse scattering problems in many…
Given a set of transmission eigenvalues, we describe the connection of such a set to the indicator functions in entire function theory. The indicator functions control the asymptotic growth rate of the solution of the Sturm-Liouville…
In this paper, we consider the inverse scattering problem associated with an inhomogeneous media with a conductive boundary. First, we discuss the inverse conductivity problem of reconstructing the conductivity parameter from scattering…
In this paper, we investigate the interior transmission eigenvalue problem for an inhomogeneous media with conductive boundary conditions. We prove the discreteness and existence of the transmission eigenvalues. We also investigate the…
Anisotropic thin sheets of materials possess intriguing properties because of their ability to modify the phase, amplitude and polarization of incident waves. Such sheets are usually modeled by imposing transmission conditions of resistive…
This paper considers the inverse problem of scattering of time-harmonic acoustic and electromagnetic plane waves by a bounded, inhomogeneous, penetrable obstacle with embedded objects inside. A new method is proposed to prove that the…
We prove a Weyl asymptotics $N(r) = c r^d + {\mathcal O}_{\epsilon}(r^{d - \kappa + \epsilon})$, $\forall\, 0< \epsilon \ll 1$, for the counting function $N(r) = \sharp\{\lambda_j \in {\mathbb C} \setminus \{0\}:\: |\lambda_j| \leq r^2\}$,…
We describe the asymptotic distribution of the eigenvalues of interior transmission problem in absorbing medium. We apply the Cartwright's theory and the technique from asymptotic periodic entire function theory. We find a Weyl's type of…
In this paper, we consider the numerical approximation of the Steklov eigenvalue problem that arises in inverse acoustic scattering. The underlying scattering problem is for an inhomogeneous isotropic medium. These eigenvalues have been…
We provide a new analytical and computational study of the transmission eigenvalues with a conductive boundary condition. These eigenvalues are derived from the scalar inverse scattering problem for an inhomogeneous material with a…
For the complex interior transmission eigenvalues (ITE) we study for small $\theta > 0$ the counting function $$N(\theta, r) = #\{\lambda \in \C:\: \lambda \: {\rm is} \: {\rm (ITE)},\: |\lambda| \leq r, \: 0 \leq \arg \lambda \leq…
We investigate an inverse scattering problem for a thin inhomogeneous scatterer in R^m, m = 2,3, which we model as a m-1 dimensional open surface. The scatterer is referred to as a screen. The goal is to design target signatures that are…
In this paper, we consider the scattering theory for acoustic-type equations on non-compact manifolds with a single flat end. Our main purpose is to show an existence result of non-scattering energies. Precisely, we show a Weyl-type lower…
The scattering phase, defined as $ \log \det S ( \lambda ) / 2\pi i $ where $ S ( \lambda ) $ is the (unitary) scattering matrix, is the analogue of the counting function for eigenvalues when dealing with exterior domains and is closely…