Limiting absorption principle for the Dirac operator
Lipschitzian norm estimate of one-dimensional Poisson equations and applications
By direct calculus we identify explicitly the lipschitzian norm of the solution of the Poisson equation in terms of various norms of g, where is a Sturm–Liouville operator or generator of a non-singular diffusion in an interval. This allows us to obtain the best constant in the L1-Poincaré inequality (a little stronger than the Cheeger isoperimetric inequality) and some sharp transportation–information inequalities and concentration inequalities for empirical means. We conclude with several illustrative...
Ljusternik-Schnirelmann theory on -manifolds
Local decay estimates for Schrödinger operators with long range potentials
Local Decay in time of solutions to Schrödinger's equation with a dilation-analytic interaction.
Local energy decay for several evolution equations on asymptotically euclidean manifolds
Let be a long range metric perturbation of the Euclidean Laplacian on , . We prove local energy decay for the solutions of the wave, Klein-Gordon and Schrödinger equations associated to . The problem is decomposed in a low and high frequency analysis. For the high energy part, we assume a non trapping condition. For low (resp. high) frequencies we obtain a general result about the local energy decay for the group where has a suitable development at zero (resp. infinity).
Local Exchange Potentials for Electronic Structure Calculations
The Hartree-Fock exchange operator is an integral operator arising in the Hartree-Fock model as well as in some instances of the density functional theory. In a number of applications, it is convenient to approximate this integral operator by a multiplication operator, i.e. by a local potential. This article presents a detailed analysis of the mathematical properties of various local approximations to the nonlocal Hartree-Fock exchange operator including the Slater potential, the optimized effective...
Local invariants of spectral asymmetry.
Local Time-Decay of High Energy Scattering States for the Schrödinger Equation.
Local uniform convergence of the Riesz means of Laplace and Dirac expansions
Localization effects for eigenfunctions near to the edge of a thin domain
Localization of spectrum bottom for the Stokes operator in a random porous medium.
Localization of Spherical Harmonic Expansions.
Locating real eigenvalues of a spectral problem in fluid-solid type structures.
Location of resonances generated by degenerate potential barrier.
Long range scattering and modified wave operators for Hartree equations
We study the theory of scattering for the Hartree equation with long range potentials. We prove the existence of modified wave operators with no size restriction on the data and we determine the asymptotic behaviour in time of solutions in the range of the wave operators.
Long range scattering with Stark effect and almost periodic potentials.
Long-range many-body scattering.
Long-range scattering of two- and three-body quantum systems
Lower bounds for pseudo-differential operators