51 citations · 53 across the 5 of their papers we have counts for
4 papers · 1 filter
Almost global existence for Hamiltonian PDEs on compact manifolds
Dario Bambusi, Joackim Bernier, Benoît Grébert +1
We prove an abstract result of almost global existence of small solutions to semi-linear Hamiltonian partial differential equations satisfying very weak non resonance conditions an…
Bernstein inequalities via the heat semigroup
Rafik Imekraz, El Maati Ouhabaz
We extend the classical Bernstein inequality to a general setting including Schr{ö}dinger operators and divergence form elliptic operators on Riemannian manifolds or domains. Moreo…
On random Hermite series
Rafik Imekraz, Didier Robert, Laurent Thomann
We study integrability and continuity properties of random series of Hermite functions. We get optimal results which are analogues to classical results concerning Fourier series, l…
Normal Forms for Semilinear Quantum Harmonic Oscillators
Benoit Grebert, Rafik Imekraz, Eric Paturel
We consider the semilinear harmonic oscillator $$iψ_t=(-Δ+\va{x}^{2} +M)ψ+\partial_2 g(ψ,\bar ψ), \quad x\in \R^d, t\in \R$$ where is a Hermite multiplier and a smooth func…