10 papers
The Schrödinger Ornstein--Uhlenbeck flow: dispersion, restriction and nonlinear dynamics
Nicola Garofalo
We study the Schrödinger evolution generated by the isotropic Ornstein--Uhlenbeck operator \[ \mathscr L=Δ-\langle x,\nabla\rangle \] in , where is the in…
Fractional operators and Sobolev spaces on homogeneous groups
Nicola Garofalo, Annunziata Loiudice, Dimiter Vassilev
We establish foundational properties of fractional operators on Lie groups of homogeneous type. We prove embedding theorems for the associated Sobolev-type spaces.
Fractal Mehler kernels and nonlinear geometric flows
Nicola Garofalo
In this paper we introduce a two-parameter family of Mehler kernels and connect them to a class of Baouendi-Grushin flows in fractal dimension. We also highlight a link with a geom…
Dispersive equations with invariant measures
Nicola Garofalo
In mathematical physics it is of interest to study Schrödinger equations with friction and possessing an invariant measure. The focus of this paper is the Cauchy problem for the Sc…
Overdetermined fractional Serrin problem
Nicola Garofalo, Dimiter Vassilev
We solve a version of the Serrin overdetermined problem for the Weinstein operator involving a Bessel operator.
Uncertainty principles for the imaginary Ornstein-Uhlenbeck operator
Nicola Garofalo
We prove two forms of uncertainty principle for the Schrödinger group generated by the Ornstein-Uhlenbeck operator. As a consequence, we derive a related (in fact, equivalent) resu…