Given a Riemannian manifold endowed with its Laplace-Beltrami operator, consider the
associated spectral projector on a thin interval. As an operator from L2 to Lp, what is its …

We study the local well-posedness of the nonlinear Schrödinger equation associated to the
Grushin operator with random initial data. To the best of our knowledge, no well-posedness …

Let $\mathcal {L} $ be the sub-Laplacian on H-type groups and $\phi:\mathbb
{R}^+\to\mathbb {R} $ be a smooth function. The primary objective of the paper is to study …

We prove Strichartz estimates for the semigroups associated to stratified and/or rotating
inviscid geophysical fluids using Fourier restriction theory. We prove new results for rotating …

In this paper, we study a class of dispersive wave equations on the Heisenberg group H n.
Based on the group Fourier transform on H n, the properties of the Laguerre functions and …

It was proved by H. Bahouri, P. G {\'e} rard and C.-J. Xu in [9] that the Schr {\" o} dinger
equation on the Heisenberg group $\mathbb {H}^ d $, involving the sublaplacian, is an …

We establish global bounds for solutions to stationary and time-dependent Schr\" odinger
equations associated with the sublaplacian $\mathcal L $ on the Heisenberg group, as well …

We prove uniform resolvent estimates in weighted $ L^ 2$-spaces for radial solutions of the
sublaplacian $\mathcal {L} $ on the Heisenberg group $\mathbb {H}^ d $. The proofs are …

Let $\Delta_\kappa $ be the Dunkl Laplacian on $\mathbb {R}^ n $ and $\phi:\mathbb
{R}^+\to\mathbb {R} $ is a smooth function. The aim of this manuscript is twofold. First, we …

In this paper, we develop the semiclassical analysis of the lowest dimensional simply
connected nilpotent Lie group of step 3, called the Engel group and denoted by ${\mathbb …