Related papers: Transmission eigenvalues for operators with consta…

We prove that a linear fractional operator with an asymptotically constant lower order term in the whole space admits eigenvalues.

This work investigates spectrum and root functions (that is, eigen- and associated functions) of a Sturm-Liouville problem involving an abstract linear operator (nonselfadjoint in general) in the equation together with supplementary…

In this paper, we give a numerical analysis for the transmission eigenvalue problem by the finite element method. A type of multilevel correction method is proposed to solve the transmission eigenvalue problem. The multilevel correction…

We transform an inverse scattering problem to be an interior transmission problem. We find an inverse uniqueness on the scatterer with a knowledge of a fixed interior transmission eigenvalue. By examining the solution in a series of…

The transmission eigenvalue problem is an important and challenging topic arising in the inverse scattering theory. In this paper, for the Helmholtz transmission eigenvalue problem, we give a weak formulation which is a nonselfadjoint…

The paper deals with a formally self-adjoint first order linear differential operator acting on m-columns of complex-valued half-densities over an n-manifold without boundary. We study the distribution of eigenvalues in the elliptic setting…

We report a new analytical method for solution of a wide class of second-order differential equations with eigenvalues replaced by arbitrary functions. Such classes of problems occur frequently in Quantum Mechanics and Optics. This approach…

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…

This paper is devoted to a dispersion analysis of a class of perturbed p-Laplacians. Besides the p-Laplacian-like eigenvalue problems we also deal with new and non-standard eigenvalue problems, which can not be solved by the methods used in…

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 work, we consider not only a discontinuous boundary-value problem with retarded argument and four supplementary transmission conditions at the two points of discontinuities but also, eigenparameter-dependent boundary conditions and…

We characterise regions in the complex plane that contain all non-embedded eigenvalues of a perturbed periodic Dirac operator on the real line with real-valued periodic potential and a generally non-symmetric matrix-valued perturbation V .…

Dirac operator eigenvalues split into two when subjected to two different external vector sources. In a specific finite-volume scaling regime of gauge theories with fermions, this problem can be mapped to a chiral Random Two-Matrix Theory.…

We consider the analytic continuation of the transfer function for a 2x2 matrix Hamiltonian into the unphysical sheets of the energy Riemann surface. We construct non-selfadjoint operators representing operator roots of the transfer…

Applying perturbation theory methods, the absence of the point spectrum for some nonselfadjoint integro-differential operators is investigated. The considered differential operators are of arbitrary order and act in either…

The aim of these notes is to describe some recent results concerning dispersive estimates for principally normal pseudodifferential operators. The main motivation for this comes from unique continuation problems. Such estimates can be used…

In this paper we consider the transmission eigenvalue problem for Maxwell's equations corresponding to non-magnetic inhomogeneities with contrast in electric permittivity that changes sign inside its support. We formulate the transmission…

In this paper we prove some results on interior transmission eigenvalues. First, under rea- sonable assumptions, we prove that the spectrum is a discrete countable set and the generalized eigenfunctions spanned a dense space in the range of…

We determine the general form of the asymptotics for Dirichlet eigenvalues of the one-dimensional linear damped wave operator. As a consequence, we obtain that given a spectrum corresponding to a constant damping term this determines the…

We consider the differential of a self-consistent transfer operator at a fixed point of the operator itself and show that its spectral properties can be used to establish a kind of local exponential convergence to equilibrium: probability…