Local operators and a characterization of the Volterra operator.
Local Operators Between Spaces of Ultradifferentiable Functions and Ultradistributions.
Local polynomials are polynomials
We prove that a function f is a polynomial if G◦f is a polynomial for every bounded linear functional G. We also show that an operator-valued function is a polynomial if it is locally a polynomial.
Local properties of accessible injective operator ideals
In addition to Pisier’s counterexample of a non-accessible maximal Banach ideal, we will give a large class of maximal Banach ideals which are accessible. The first step is implied by the observation that a “good behaviour” of trace duality, which is canonically induced by conjugate operator ideals can be extended to adjoint Banach ideals, if and only if these adjoint ideals satisfy an accessibility condition (theorem 3.1). This observation leads in a natural way to a characterization of accessible...
Local Properties of Taylor's Analytic Functional Calculus.
Local properties of the solution set of the operator equation in Banach spaces in a neighbourhood of a bifurcation point
In this work we study the problem of the existence of bifurcation in the solution set of the equation F(x, λ)=0, where F: X×R k →Y is a C 2-smooth operator, X and Y are Banach spaces such that X⊂Y. Moreover, there is given a scalar product 〈·,·〉: Y×Y→R 1 that is continuous with respect to the norms in X and Y. We show that under some conditions there is bifurcation at a point (0, λ0)∈X×R k and we describe the solution set of the studied equation in a small neighbourhood of this point.
Local Reflexivity and (p, g)-Summing Maps.
Local Riesz transform characterization of local Hardy spaces
Local spectral radius formula for operators in Banach spaces
Local spectral theory for operator matrices.
Local spectral theory of shifts with operator-valued weights. (Sur la théorie spectrale locale des shifts à poids opérateurs.)
Local spectrum and Kaplansky's theorem on algebraic operators
Using elementary arguments we improve former results of P. Vrbová concerning local spectrum. As a consequence, we obtain a new proof of Kaplansky’s theorem on algebraic operators on a Banach space.
Local spectrum and local spectral radius of an operator at a fixed vector
Let be a complex Banach space and e ∈ a nonzero vector. Then the set of all operators T ∈ ℒ() with , respectively , is residual. This is an analogy to the well known result for a fixed operator and variable vector. The results are then used to characterize linear mappings preserving the local spectrum (or local spectral radius) at a fixed vector e.
Local structure of the zero-sets of differentiable mappings and application to bifurcation theory.
Local Time-Decay of High Energy Scattering States for the Schrödinger Equation.
Local Toeplitz operators based on wavelets: phase space patterns for rough wavelets
We consider two standard group representations: one acting on functions by translations and dilations, the other by translations and modulations, and we study local Toeplitz operators based on them. Local Toeplitz operators are the averages of projection-valued functions , where for a fixed function ϕ, denotes the one-dimensional orthogonal projection on the function , U is a group representation and g is an element of the group. They are defined as integrals , where W is an open, relatively...
Local uniform linear convexity with respect to the Kobayashi distance.
Localisation for non-monotone Schrödinger operators
We study localisation effects of strong disorder on the spectral and dynamical properties of (matrix and scalar) Schrödinger operators with non-monotone random potentials, on the -dimensional lattice. Our results include dynamical localisation, i.e. exponentially decaying bounds on the transition amplitude in the mean. They are derived through the study of fractional moments of the resolvent, which are finite due to resonance-diffusing effects of the disorder. One of the byproducts of the analysis...
Localisation pour des opérateurs de Schrödinger aléatoires dans : un modèle semi-classique
Dans , nous démontrons un résultat de localisation exponentielle pour un opérateur de Schrödinger semi-classique à potentiel périodique perturbé par de petites perturbations aléatoires indépendantes identiquement distribuées placées au fond de chaque puits. Pour ce faire, on montre que notre opérateur, restreint à un intervalle d’énergie convenable, est unitairement équivalent à une matrice aléatoire infinie dont on contrôle bien les coefficients. Puis, pour ce type de matrices, on prouve un résultat...
Localization of Singular Integral Operators.