Erratum to “Non-trapping condition for semiclassical Schrödinger operators with matrix-valued potentials”.
Error estimate in the generalized Szegö theorem
Error estimates for the Coupled Cluster method
The Coupled Cluster (CC) method is a widely used and highly successful high precision method for the solution of the stationary electronic Schrödinger equation, with its practical convergence properties being similar to that of a corresponding Galerkin (CI) scheme. This behaviour has for the discrete CC method been analyzed with respect to the discrete Galerkin solution (the “full-CI-limit”) in [Schneider, 2009]. Recently, we globalized the CC formulation to the full continuous space, giving a root...
Essential self-adjointness for magnetic Schrödinger operators on non-compact manifolds
We give a condition of essential self-adjointness for magnetic Schrödinger operators on non-compact Riemannian manifolds with a given positive smooth measure which is fixed independently of the metric. This condition is related to the classical completeness of a related classical hamiltonian without magnetic field. The main result generalizes the result by I. Oleinik [29,30,31], a shorter and more transparent proof of which was provided by the author in [41]. The main idea, as in [41], consists...
Essential Selfadjointness of Dirac Operators with a Strongly Singular Potential.
Essential self-adjointness of symmetric linear relations associated to first order systems
The purpose of this note is to present several criteria for essential self-adjointness. The method is based on ideas due to Shubin. This note is divided into two parts. The first part deals with symmetric first order systems on the line in the most general setting. Such a symmetric first order system of differential equations gives rise naturally to a symmetric linear relation in a Hilbert space. In this case even regularity is nontrivial. We will announce a regularity result and discuss criteria...
Estimates for a number of negative eigenvalues of the Schrödinger operator with intensive magnetic field
Estimates for second order derivatives of eigenvectors in thin anisotropic plates with variable thickness.
Estimates for the Asymptotic Behavior of Solutions of the Helmholtz Equation, with an Application to Second order Elliptic Differential Operators with Variable Coefficients.
Estimates for the asymptotic behavior of solutions of the Helmholtz equation, with an application to second order elliptic differential operators with variable coefficients (Erratum).
Estimates for the Classical Parametrix for the Laplacian.
Estimates for the cut-off resolvent of the Laplacian for trapping obstacles
Estimates for the first eigenfunction of linear eigenvalue problems via Steiner symmetrization.
Estimates of eigenvalues and eigenfunctions in periodic homogenization
For a family of elliptic operators with rapidly oscillating periodic coefficients, we study the convergence rates for Dirichlet eigenvalues and bounds of the normal derivatives of Dirichlet eigenfunctions. The results rely on an estimate in for solutions with Dirichlet condition.
Estimates of the first eigenvalue of a big cup domain of a 2-sphere
Estimates of the heat content on a class of domains.
Estimates of the principal eigenvalue of the -Laplacian and the -biharmonic operator
We survey recent results concerning estimates of the principal eigenvalue of the Dirichlet -Laplacian and the Navier -biharmonic operator on a ball of radius in and its asymptotics for approaching and . Let tend to . There is a critical radius of the ball such that the principal eigenvalue goes to for and to for . The critical radius is for any for the -Laplacian and in the case of the -biharmonic operator. When approaches , the principal eigenvalue of the Dirichlet...
Estimates on the number of scattering poles near the real axis for strictly convex obstacles
For the Dirichlet Laplacian in the exterior of a strictly convex obstacle, we show that the number of scattering poles of modulus in a small angle near the real axis, can be estimated by Const for sufficiently large depending on . Here is the dimension.
Estimation des résidus de la matrice de diffusion associés à des résonances de forme I
Estimation des valeurs propres d'opérateurs elliptiques sur des ouverts non bornés