75 citations · 484 across the 32 of their papers we have counts for
9 papers · 1 filter
Spectral summability for the quartic oscillator with applications to the Engel group
Hajer Bahouri, Davide Barilari, Isabelle Gallagher +1
In this article, we investigate spectral properties of the sublaplacian on the Engel group, which is the main example of a Carnot group of step 3. We develop a new approac…
Strichartz estimates and Fourier restriction theorems on the Heisenberg group
Hajer Bahouri, Davide Barilari, Isabelle Gallagher
This paper is dedicated to the proof of Strichartz estimates on the Heisenberg group for the linear Schrödinger and wave equations involving the sublaplacian. The Sc…
Kolmogorov-Fokker-Planck operators in dimension two: heat kernel and curvature
Davide Barilari, Francesco Boarotto
We consider the heat equation associated with a class of hypoelliptic operators of Kolmogorov-Fokker-Planck type in dimension two. We explicitly compute the first meaningful coeffi…
Heat kernel asymptotics on sub-Riemannian manifolds with symmetries and applications to the bi-Heisenberg group
Davide Barilari, Ugo Boscain, Robert W. Neel
By adapting a technique of Molchanov, we obtain the heat kernel asymptotics at the sub-Riemannian cut locus, when the cut points are reached by an -dimensional parametric family…
Curvature terms in small time heat kernel expansion for a model class of hypoelliptic Hörmander operators
Davide Barilari, Elisa Paoli
We consider the heat equation associated with a class of second order hypoelliptic Hörmander operators with constant second order term and linear drift. We describe the possible sm…
On the heat diffusion for generic Riemannian and sub-Riemannian structures
Davide Barilari, Ugo Boscain, Grégoire Charlot +1
In this paper we provide the small-time heat kernel asymptotics at the cut locus in three relevant cases: generic low-dimensional Riemannian manifolds, generic 3D contact sub-Riema…