La distribution des pôles de la matrice de diffusion
Large atoms in large magnetic fields
Lieb–Thirring inequalities with improved constants
Following Eden and Foias we obtain a matrix version of a generalised Sobolev inequality in one dimension. This allows us to improve on the known estimates of best constants in Lieb–Thirring inequalities for the sum of the negative eigenvalues for multidimensional Schrödinger operators.
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...
Localization of spectrum bottom for the Stokes operator in a random porous medium.
Location of resonances generated by degenerate potential barrier.
Lower bounds for pseudo-differential operators
This paper contains some new results on lower bounds for pseudo-differential operators whose symbols do not remain positive. Non-negativity of averages of the symbol on canonical images of the unit ball is sufficient to get a Gårding type inequality for Schrödinger operators with magnetic potential and one dimensional pseudo-differential operators.
Lower bounds for Schrödinger equations
Lower bounds for Schrödinger operators in H¹(ℝ)
We prove trace inequalities of type where , under suitable hypotheses on the sequences and , with the first sequence increasing and the second bounded.
Lower bounds for the infimum of the spectrum of the Schrödinger operator in and the Sobolev inequalities.