相关论文: A limiting absorption principle for Helmholtz syst…

In this paper, we shall show that the limiting absorption principle for the wave operator on the asymptotically Minkowski spacetime. This problem was previously considered by [A. Vasy, J. Spect. Theory, 10,439-461 , (2020)]. Here, we employ…

In this paper, we investigate whether Variational Principles can be associated with the Helmholtz equation subject to impedance (absorbing) boundary conditions. This model has been extensively studied in the literature from both…

We study the one-dimensional Helmholtz equation with (possibly perturbed) quasiperiodic coefficients. Quasiperiodic functions are the restriction of higher dimensional periodic functions along a certain (irrational) direction. In classical…

We provide a limiting absorption principle for the self-adjoint realizations of Laplace operators corresponding to boundary conditions on (relatively open parts $\Sigma$ of) compact hypersurfaces $\Gamma=\partial\Omega$,…

We prove the limiting absorption principle and discuss the continuity properties of the boundary values of the resolvent for a class of form bounded perturbations of the Euclidean Laplacian $\Delta$ that covers both short and long range…

The limiting absorption principle in two-dimensional space is justified for a second-order elliptic operators. Necessary and sufficient conditions for the right-hand side are given for this principle to be valid.

In this paper, we examine the discrete Laplacian acting on a hexagonal lattice by introducing long-range modifications in both the metric and the potential. Our objective is to establish a Limiting Absorption Principle, excluding possible…

This paper concerns the quantitative step of the medical imaging modality Thermo-acoustic Tomography (TAT). We model the radiation propagation by a system of Maxwell's equations. We show that the index of refraction of light and the…

In this paper we consider Dirac operators in $\mathbb R^n$, $n\geq2$, with a potential $V$. Under mild decay and continuity assumptions on $V$ and some spectral assumptions on the operator, we prove a limiting absorption principle for the…

We show global-in-time Strichartz estimates for the isotropic Maxwell system with divergence free data. On the scalar permittivity and permeability we impose decay assumptions as $|x|\to\infty$ and a non-trapping condition. The proof is…

We apply weighted Mourre commutator theory to prove the limiting absorption principle for the discrete Schr{\"o}dinger operator perturbed by the sum of a Wigner-von Neumann and long-range type potential. In particular, this implies a new…

We investigate quantitative (or effective) versions of the limiting absorption principle, for the Schr\"odinger operator on asymptotically conic manifolds with short-range potentials, and in particular consider estimates of the form $$ \|…

We examine the discrete Laplacian acting on a triangular lattice, introducing long-range perturbations to both the metric and the potential. Our goal is to establish a Limiting Absorption Principle away from possible embedded eigenvalues.…

We study decay rates for bounded $C_0$-semigroups from the perspective of $L^p$-infinite-time admissibility and related resolvent estimates. In the Hilbert space setting, polynomial decay of semigroup orbits is characterized by the…

Numerical discretization of the large-scale Maxwell's equations leads to an ill-conditioned linear system that is challenging to solve. The key requirement for successive solutions of this linear system is to choose an efficient solver. In…

We investigate the representations of the solutions to Maxwell's equations based on the combination of hypercomplex function-theoretical methods with quantum mechanical methods. Our approach provides us with a characterization for the…

Effective non-Hermitian Hamiltonians are obtained to describe coherent perfect absorbing and lasing boundary conditions. PT -symmetry of the Hamiltonians enables to design configurations which perfectly absorb at multiple frequencies.…

From the Hamiltonian connecting the inside and outside of an Fabry-Perot cavity, which is derived from the Maxwell boundary conditions at a mirror of the cavity, a master equation of a non-Lindblad form is derived when the cavity embeds…

The main result of the article is validity of the limiting absorption principle and thus absence of the singular continuous spectrum for compact quantum graphs with several infinite leads attached. The technique used involves…

Most finite element methods for solving time-harmonic wave-propagation problems lead to a linear system with a non-normal coefficient matrix. The non-normality is due to boundary conditions and losses. One way to solve these systems is to…