Related papers: Relative stability of singular spectrum
For a stationary sequence that is regularly varying and associated we give conditions which guarantee that partial sums of this sequence, under normalization related to the exponent of regular variation, converge in distribution to a…
We establish sharp stability results for of non--selfadjoint the ascent and descent spectra under strong resolvent convergence (SRS), a natural framework for finite element approximations of non-selfadjoint and singularly perturbed…
We show that a derivator is stable if and only if homotopy finite limits and homotopy finite colimits commute, if and only if homotopy finite limit functors have right adjoints, and if and only if homotopy finite colimit functors have left…
In this paper, we study singularities of the Lagrangian fibration given by a completely integrable system. We prove that a non-degenerate singular fibre satisfying the so-called connectedness condition is structurally stable under (small…
We establish sharp well-posedness and approximation estimates for variational saddle point systems at the continuous level. The main results of this note have been known to be true only in the finite dimensional case. Known spectral results…
This paper considers the problem of robust stability for a class of uncertain quantum systems subject to unknown perturbations in the system coupling operator. A general stability result is given for a class of perturbations to the system…
This paper is devoted to the study of essential self-adjointness of a relativistic Schr\"{o}dinger operator with a singular homogeneous potential. From an explicit condition on the coefficient of the singular term, we provide a sufficient…
We derive the formula for the stationary states of particle-number conserving exclusion processes infinitesimally perturbed by inhomogeneous adsorption and desorption. The formula not only proves but also generalises the conjecture proposed…
We call a positive real number $\lambda$ admissible if it belongs to the Lagrange spectrum and there exists an irrational number $\alpha$ such that $\mu(\alpha)=\lambda$. Here $\mu(\alpha)$ denotes the Lagrange constant of $\alpha$ -…
We consider the plasmonic eigenvalue problem for a general 2D domain with a curvilinear corner, studying the spectral theory of the Neumann--Poincar\'e operator of the boundary. A limiting absorption principle is proved, valid when the…
We investigate branched PT-symmetric optical lattices. We consider both the linear and nonlinear Schr\"odinger equations with a PT-symmetric periodic potential on the graph and solve them by imposing weighted vertex boundary conditions. A…
Within the framework of the hypothesis offered by authors about a complex-valued nature of physical quantities the stability of basic equations of the classical physics concerning complex-valued perturbations of parameters and boundary…
A commonly used approach to study stability in a complex system is by analyzing the Jacobian matrix at an equilibrium point of a dynamical system. The equilibrium point is stable if all eigenvalues have negative real parts. Here, by…
We introduce an arbitrary order, stabilized finite element method for solving a unique continuation problem subject to the time-harmonic elastic wave equation with variable coefficients. Based on conditional stability estimates we prove…
We discuss the spectral subspace perturbation problem for a self-adjoint operator. Assuming that the convex hull of a part of its spectrum does not intersect the remainder of the spectrum, we establish an \textit{a priori} sharp bound on…
We introduce a novel framework for the stability analysis of discrete-time linear switching systems with switching sequences constrained by an automaton. The key element of the framework is the algebraic concept of multinorm, which…
We review some results on the spectral theory of Schr{\"o}dinger and Dirac operators. We focus on two aspects: the existence of embbedded eigen-values in the essential spectrum and the limiting absorption principle. They both are important…
We study the spectrum of a one-dimensional Schroedinger operator perturbed by a fast oscillating potential. The oscillation period is a small parameter. The essential spectrum is found in an explicit form. The existence and multiplicity of…
We prove an abstract criterion on spectral instability of nonnegative selfadjoint extensions of a symmetric operator and apply this to self-adjoint Neumann Laplacians on bounded Lipschitz domains, intervals, and graphs. Our results can be…
We consider a two-dimensional nonlinear waveguide with distributed gain and losses. The optical potential describing the system consists of an unperturbed complex potential depending only on one transverse coordinate, i.e., corresponding to…