Absence of eigenvalues for integro-differential operators with periodic coefficients.
Absolute continuity and hyponormal operators.
Almost commuting Hermitian matrices.
An a posteriori Error Estimation of the Rayleigh-Ritz Eigenvalues.
An Iteration Method for Studying the Bifurcation of Solutions of the Nonlinear Equations, L(...) u + ..R (..., u) = 0 .
Analyse spectrale des formes automorphes et séries d'Eisenstein.
Analytic families of semigroups.
Analytic Perturbation of Semi-Fredholm Operators.
Analytic Set-Valued Functions and Spectra.
Approximation of eigenvalues for unbounded Jacobi matrices using finite submatrices
We consider an infinite Jacobi matrix with off-diagonal entries dominated by the diagonal entries going to infinity. The corresponding self-adjoint operator J has discrete spectrum and our purpose is to present results on the approximation of eigenvalues of J by eigenvalues of its finite submatrices.
Approximation the Shift with Toeplitz Operators.
Ascent spectrum and essential ascent spectrum
We study the essential ascent and the related essential ascent spectrum of an operator on a Banach space. We show that a Banach space X has finite dimension if and only if the essential ascent of every operator on X is finite. We also focus on the stability of the essential ascent spectrum under perturbations, and we prove that an operator F on X has some finite rank power if and only if for every operator T commuting with F. The quasi-nilpotent part, the analytic core and the single-valued extension...
Asymptotics of the integrated density of states for periodic elliptic pseudo-differential operators in dimension one.
We consider a periodic pseudo-differential operator on the real line, which is a lower-order perturbation of an elliptic operator with a homogeneous symbol and constant coefficients. It is proved that the density of states of such an operator admits a complete asymptotic expansion at large energies. A few first terms of this expansion are found in a closed form.
Asymptotique de la phase de diffusion à haute énergie pour des perturbations du second ordre du laplacien
a-Weyl's theorem and perturbations
We study the stability of a-Weyl's theorem under perturbations by operators in some known classes. We establish in particular that if T is a finite a-isoloid operator, then a-Weyl's theorem is transmitted from T to T + R for every Riesz operator R commuting with T.
Best Fredholm perturbation theorems
B-Fredholm and Drazin invertible operators through localized SVEP
Let be a Banach space and be a bounded linear operator on . We denote by the set of all complex such that does not have the single-valued extension property at . In this note we prove equality up to between the left Drazin spectrum, the upper semi-B-Fredholm spectrum and the semi-essential approximate point spectrum. As applications, we investigate generalized Weyl’s theorem for operator matrices and multiplier operators.
Bifurcation for the solutions of equations involving set valued mappings.
Browder's theorems and the spectral mapping theorem.
Classes of operators satisfying a-Weyl's theorem
In this article Weyl’s theorem and a-Weyl’s theorem on Banach spaces are related to an important property which has a leading role in local spectral theory: the single-valued extension theory. We show that if T has SVEP then Weyl’s theorem and a-Weyl’s theorem for T* are equivalent, and analogously, if T* has SVEP then Weyl’s theorem and a-Weyl’s theorem for T are equivalent. From this result we deduce that a-Weyl’s theorem holds for classes of operators for which the quasi-nilpotent part H₀(λI...