相关论文: Absolutely continuous spectrum of Stark operators

In this paper, we study the asymptotic stability of smooth 1-solitons in the Degasperis-Procesi (DP) equation. Such solutions necessarily exist on a non-zero background, and their spectral and orbital stability has previously been verified…

We study spectral properties of bounded and unbounded complex Jacobi matrices. In particular, we formulate conditions assuring that the spectrum of the studied operators is continuous on some subsets of the complex plane and we provide…

In this paper, we prove that for any $d$-frequency analytic quasiperiodic Schr\"odinger operator, if the frequency is weak Liouvillean, and the potential is small enough, then the corresponding operator has absolutely continuous spectrum.…

I prove that quasi-periodic Schr\"odinger operators in arbitrary dimension have some absolutely continuous spectrum.

This paper establishes the spectral stability of monotone traveling front solutions for reaction-diffusion equations where the reaction function is of Nagumo (or bistable) type and with diffusivities which are density dependent and…

We give a new proof of a version of Klein's theorem on the existence of absolutely continuous spectrum for the Anderson model on the Bethe Lattice at weak disorder.

The classical one-phase Stefan problem (without surface tension) allows for a continuum of steady state solutions, given by an arbitrary (but sufficiently smooth) domain together with zero temperature. We prove global-in-time stability of…

We extend in this work the Jitomirskaya-Last inequality and Last-Simoncriterion for the absolutely continuous spectral component of a half-line Schr\"odinger operator to the special class of matrix-valued Jacobi operators…

Almost commutative models provide a framework for Connes' work on the standard model of particle physics. These models are constructed as products of a the canonical spectral triple of a compact connected spin manifold with a finite…

The structure of the spectrum of random operators is studied. It is shown that if the density of states measure of some subsets of the spectrum is zero, then these subsets are empty. In particular follows that absolute continuity of the IDS…

We consider steady surface waves in an infinitely deep two--dimensional ideal fluid with potential flow, focusing on high-amplitude waves near the steepest wave with a 120 degree corner at the crest. The stability of these solutions with…

It is well-established that the spectral measure for one-frequency Schr\"odinger operators with Diophantine frequencies exhibits optimal $1/2$-H\"older continuity within the absolutely continuous spectrum. This study extends these findings…

This paper addresses the stability analysis of infinite-dimensional sampled-data systems under unbounded perturbations. We present two classes of unbounded perturbations preserving the exponential stability of sampled-data systems. To this…

In this paper we prove that a class of non self-adjoint second order differential operators acting in cylinders $\Omega\times\mathbb R\subseteq\mathbb R^{d+1}$ have only real discrete spectrum located to the right of the right most point of…

For Schr\"odinger operator $H=-\Delta+ V({\mathbf x})\cdot$, acting in the space $L_2(\mathbb R^d)\,(d\ge 3)$, necessary and sufficient conditions for semi-boundedness and discreteness of its spectrum.are obtained without assumption that…

We analyse the spectral phase diagram of Schr\"odinger operators $ T +\lambda V$ on regular tree graphs, with $T$ the graph adjacency operator and $V$ a random potential given by iid random variables. The main result is a criterion for the…

The primary objective of this paper is to generalize the results of [arXiv:2111.03548] to the case of quasi-smooth Berkovich curves by establishing a connection between the spectrum and the radii of convergence. To achieve this, we…

In our manuscript, we develop a new approach for stability analysis of one-dimensional wave equation with time delay. The major contribution of our work is to develop a new method for spectral analysis. We derive sufficient and necessary…

The aim of the paper is firstly to study domains of definitions in terms of boundary conditions of minimal and maximal operators, as well as selfadjoint extensions of a minimal operator associated with the fourth-order differential operator…

We look at invariance of a.e. boundary condition spectral behavior under perturbations, $W$, of half-line, continuum or discrete Schr\"odinger operators. We extend the results of del Rio, Simon, Stolz from compactly supported $W$'s to…