Related papers: The stability radius of linear operator pencils

Utilizing the stability characterizations of generalized inverses of linear operator, we investigate the existence of generalized resolvents of linear pencils in Banach spaces. Some practical criterions for the existence of generalized…

Operators possessing analytic generalized inverses satisfying the resolvent identity are studied. Several characterizations and necessary conditions are obtained. The maximal radius of regularity for a Fredholm operator T is computed in…

We prove that if T is an operator on an infinite-dimensional Hilbert space whose spectrum and essential spectrum are both connected and whose Fredholm index is only 0 or 1, then the only nontrivial norm-stable invariant subspaces of T are…

Continuing a line of investigation initiated in [11] exploring the connections between Jost and Evans functions and (modified) Fredholm determinants of Birman-Schwinger type integral operators, we here examine the stability index, or sign…

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…

The stability radius for finitely many interconnected linear exponentially stable well-posed systems with respect to static perturbations is studied. If the output space of each system is finite-dimensional, then a lower bound for the…

We study the backward stability of running a backward stable eigenstructure solver on a pencil $S(\lambda)$ that is a strong linearization of a rational matrix $R(\lambda)$ expressed in the form $R(\lambda)=D(\lambda)+ C(\lambda…

We study spectral instability of steady states to the linearized 2D Euler equations on the torus written in vorticity form via certain Birman-Schwinger type operators $K_{\lambda}(\mu)$ and their associated 2-modified perturbation…

We study the stability of Fredholm property for regular operators on Hilbert $C^*$-modules under some certain perturbations. We treat this problem when perturbing operators are (relatively) bounded or relatively compact. We also consider…

We introduce a numerical method to determine the stability of stationary pulse solutions of the complex Ginzburg-Landau equation. The method involves the computation of the point spectrum of the first-order linear differential operator with…

Withdrawn due to a likely error with the homeomorphism at line (4). Old abstract: In the monograph 'Limit Operators and their Applications in Operator Theory', the authors define the operator spectrum of a band-dominated operator T and…

Denote by $T_n^d(A)$ an upper triangular operator matrix of dimension $n$ whose diagonal entries $D_i$ are known, where $A=(A_{ij})_{1\leq i<j\leq n}$ is an unknown tuple of operators. This article is aimed at investigation of defect…

We prove a stability version of a general result that bounds the permanent of a matrix in terms of its operator norm. More specifically, suppose $A$ is an $n \times n$ matrix over $\mathbb{C}$ (resp. $\mathbb{R}$), and let $\mathcal{P}$…

Let $\mu$ be a non-negative Radon measure on ${\mathbb R}^d$ which only satisfies the polynomial growth condition. Let ${\mathcal Y}$ be a Banach space and $H^1(\mu)$ the Hardy space of Tolsa. In this paper, the authors prove that a linear…

We consider a bounded linear operator $T$ on a complex Banach space $X$ and show that its spectral radius $r(T)$ satisfies $r(T) < 1$ if all sequences $(< x',T^nx>)_{n \in \mathbb{N}_0}$ ($x \in X$, $x' \in X'$) are, up to a certain…

We consider real-analytic maps of the interval $I=[0,1]$ which are expanding everywhere except for a neutral fixed point at 0. We show that on a certain function space the spectrum of the associated Perron-Frobenius operator ${\cal M}$ has…

In this paper, we address the existence of Fredholm backstepping transformations for self-adjoint and skew-adjoint operators $A$. Under suitable assumptions on the operator $A$ and the possibly unbounded control operator $B$, we prove the…

The inner plethysm of symmetric functions corresponds to the $\lambda$-ring operations of the representation ring $R({\mathfrak S}_n)$ of the symmetric group. It is known since the work of Littlewood that this operation possesses stability…

We obtain H\"older stability estimates for the inverse Steklov and Calder\'on problems for Schr\"odinger operators corresponding to a special class of $L^2$ radial potentials on the unit ball. These results provide an improvement on earlier…

In this paper we study spectra and Fredholm properties of Ornstein-Uhlenbeck operators $$\mathcal{L}v(x)=A\triangle v(x)+\langle Sx,\nabla v(x)\rangle+Df(v_{\star}(x))v(x),\,x\in\mathbb{R}^d,\,d\geqslant 2$$ where…