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Long range scattering and modified wave operators for Hartree equations

Jean Ginibre, Giorgio Velo (1999)

Journées équations aux dérivées partielles

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.

Lower bounds for pseudo-differential operators

Nicolas Lerner, Jean Nourrigat (1990)

Annales de l'institut Fourier

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 operators in H¹(ℝ)

Ronan Pouliquen (1999)

Studia Mathematica

We prove trace inequalities of type | | u ' | | L 2 2 + ∑ j ∈ ℤ k j | u ( a j ) | 2 ≥ λ | | u | | L 2 2 where u ∈ H 1 ( ℝ ) , under suitable hypotheses on the sequences a j j ∈ ℤ and k j j ∈ ℤ , with the first sequence increasing and the second bounded.

Currently displaying 561 – 580 of 1562