A characterization of the eigenvalues of a completely continuous selfadjoint operator
A general homogenization result of spectral problem for linearized elasticity in perforated domains
The goal of this paper is to establish a general homogenization result for linearized elasticity of an eigenvalue problem defined over perforated domains, beyond the periodic setting, within the framework of the -convergence theory. Our main homogenization result states that the knowledge of the fourth-order tensor , the -limit of , is sufficient to determine the homogenized eigenvalue problem and preserve the structure of the spectrum. This theorem is proved essentially by using Tartar’s method...
A minimax principle for eigenvalues in spectral gaps: Dirac operators with Coulomb potentials.
A note on the asymptotics of perturbed expanding maps.
A perturbation theory of resonances
A relation between the multiplicity of the second eigenvalue of a graph Laplacian, Courant's nodal line theorem and the substantial dimension of tight polyhedral surfaces.
A Remark on Perturbations of Compact Operators.
A spectral perturbation problem and its applications to waves above an underwater ridge.
Abschätzungen für den zweiten Eigenwert eines positiven Operators.
Absence of eigenvalues for integro-differential operators with periodic coefficients.
Absolute continuity for Jacobi matrices with power-like weights
This work deals with a class of Jacobi matrices with power-like weights. The main theme is spectral analysis of matrices with zero diagonal and weights where α ∈ (0,1]. Asymptotic formulas for generalized eigenvectors are given and absolute continuity of the matrices considered is proved. The last section is devoted to spectral analysis of Jacobi matrices with qₙ = n + 1 + (-1)ⁿ and .
Accurate eigenvalue asymptotics for the magnetic Neumann Laplacian
Motivated by the theory of superconductivity and more precisely by the problem of the onset of superconductivity in dimension two, many papers devoted to the analysis in a semi-classical regime of the lowest eigenvalue of the Schrödinger operator with magnetic field have appeared recently. Here we would like to mention the works by Bernoff-Sternberg, Lu-Pan, Del Pino-Felmer-Sternberg and Helffer-Morame and also Bauman-Phillips-Tang for the case of a disc. In the present paper we settle one important...
An approximative solution of the generalized eigenvalue problem
Antieigenvectors of the generalized problem and an operator inequality complementary to Schwarz's inequality.
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.
Asymptotische Fehlerschranken für Rayleigh-Ritz-Approximationen selbstadjungierter Eigenwertaufgaben.
Bound states of a converging quantum waveguide
We consider a two-dimensional quantum waveguide composed of two semi-strips of width 1 and 1 − ε, where ε > 0 is a small real parameter, i.e. the waveguide is gently converging. The width of the junction zone for the semi-strips is 1 + O(√ε). We will present a sufficient condition for the existence of a weakly coupled bound state below π2, the lower bound of the continuous spectrum. This eigenvalue in the discrete spectrum is unique and its asymptotics is constructed and justified when ε → 0+....
Bounds for the singular values of smooth kernels
Completeness of the system of root functions of boundary value problems for elliptic equations with boundary conditions of Bitsadze-Samarskij type.
Comportement asymptotique de la distribution des valeurs propres de l'équation de Schrödinger associé à certains champs magnétiques sur un cylindre