Systems with exponential eigenfunctions and exponential-input/constant-output operators

Ferreira : Nonlinear Systems and Exponential Eigenfunctions

Exponential decay of eigenfunctions of Brown–Ravenhall operators

We prove the exponential decay of eigenfunctions of reductions of Brown– Ravenhall operators to arbitrary irreducible representations of rotation–reflection and permutation symmetry groups under the assumption that the corresponding eigenvalues are below the essential spectrum.

Eigenvalue Asymptotics and Exponential Decay of Eigenfunctions for Schrödinger Operators with Magnetic Fields

We consider the Schrödinger operator with magnetic field, H = ( 1 i ∇−a (x)) + V (x) in R. Assuming that V ≥ 0 and |curla |+ V + 1 is locally in certain reverse Hölder class, we study the eigenvalue asymptotics and exponential decay of eigenfunctions. Introduction Consider the Schrödinger operator with magnetic field H = H( ⇀ a , V ) = ( 1 i ∇−a (x) )2 + V (x) in R, n ≥ 3, (0.1) where i = √ −1,...

Exponential Stability and Exponential Dichotomy of Semigroups of Linear Operators

The aim of this paper is to establish necessary and sufficient conditions for exponential stability of semigroups of linear operators and to show how this conditions can be applied in order to characterize the exponential dichotomy. First, we prove that an exponentially bounded semigroup is exponentially stable if and only if it is (l(N, X), l∞(N, X))-stable, where p ∈ (1,∞). After that this re...

Essential spectra and exponential estimates of eigenfunctions of lattice operators of quantum mechanics

This paper is devoted to estimates of the exponential decay of eigenfunctions of difference operators on the lattice Zn which are discrete analogs of the Schrödinger, Dirac and square-root Klein-Gordon operators. Our investigation of the essential spectra and the exponential decay of eigenfunctions of the discrete spectra is based on the calculus of the so-called pseudodifference operators (i.e...