Related papers: Transmission Eigenvalues in One Dimension
We study an inverse uniqueness with a knowledge of spectral data in the interior transmission problem defined by an index of refraction in a simple domain. We expand the solution in such a domain into a series of one dimensional problems.…
We study the localization of the interior transmission eigenvalues (ITEs) in the case when the domain is the unit ball $\{x \in {\mathbb R}^d:\: |x| \leq 1\}, \: d\geq 2,$ and the coefficients $c_j(x), \: j =1,2,$ and the indices of…
In this paper we give results on the counting function associated with the interior transmission eigenvalues. For a complex refraction index we estimate of the counting function by Ctn. In the case where the refraction index is positive we…
In this paper we extend the results in [16] to more general domains. More precisely, we obtain transmission eigenvalue-free regions for the interior transmission problem with one complex-valued refraction index, that is, with a damping term…
We consider the anisotropic interior transmission problem with one complex-valued refraction index. Under the condition that all geodesics reach the boundary in a finite time, we obtain large regions near the real axis free of transmission…
The impact of surface reflection on the statistics of transmission eigenvalues is a largely unexplored subject of fundamental and practical importance in statistical optics. Here, we develop a first-principles theory and confirm numerically…
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…
A set of regularly distributed transmission eigenvalues generates a density function. We use such a density function inversely determines the form of the indicator function. Using the entire function theory, we reduce an uniqueness problem…
This paper investigates properties of complex-valued eigenvalue trajectories for the interior transmission problem parametrized by the index of refraction for homogeneous media. Our theoretical analysis for the unit disk shows that the only…
We study the location of the transmission eigenvalues in the isotropic case when the restrictions of the refraction indices on the boundary coincide. Under some natural conditions we show that there exist parabolic transmission…
We present two uniqueness results for the inverse problem of determining an index of refraction by the corresponding acoustic far-field measurement encoded into the scattering amplitude. The first one is a local uniqueness in determining a…
A stabilized version of the fundamental solution method to catch ill-conditioning effects is investigated with focus on the computation of complex-valued elastic interior transmission eigenvalues in two dimensions for homogeneous and…
We extend classical time-frequency limiting analysis, historically applied to one-dimensional finite signals, to the multidimensional discrete setting. This extension is relevant for images, videos, and other multidimensional signals, as it…
Light propagation through a normal medium is determined not only by the real part of the refractive index but also by its imaginary part, which represents optical gain and loss. Therefore, two media with different gain and loss landscapes…
In this paper we study the interior transmission problem and transmission eigenvalues for multiplicative perturbations of linear partial differential operator of order $\ge 2$ with constant real coefficients. Under suitable growth…
We analyze an approximate interior transmission eigenvalue problem in ${\mathbb R}^d$ for $d=2$ or $d=3$, motivated by the transmission problem of a transformation optics-based cloaking scheme and obtained by replacing the refractive index…
In this paper we show that the eigenfunctions can be found exactly for systems whose delay-Doppler spread function is concentrated along a straight line and they can be found in approximate sense for systems having a spread function…
Because the desire to explore opaque materials is ordinarily frustrated by multiple scattering of waves, attention has focused on the transmission matrix of the wave field. This matrix gives the fullest account of transmission and…
Given a Fourier transformable measure in two dimensions, we find a formula for the intensity of its Fourier transform along circles. In particular, we obtain a formula for the diffraction measure along a circle in terms of the…
For the direct problem, we give the asymptotic distribution of the (real and non-real) transmission eigenvalues for the Schrodinger operator on the half line. For the inverse problem, we prove that the potential can be uniquely determined…