Viviana Grasselli

collaborators

4 papers

math-ph2025

Propagation Estimates for the Boson Star Equation

Sébastien Breteaux, Jérémy Faupin, Viviana Grasselli

We consider the boson star equation with a general two-body interaction potential $w$ and initial data $ψ_{0}$ in a Sobolev space. Under general assumptions on $w$ , namely that $w$ d…

math-ph2025

Exponential Decay outside of the Light Cone for the Pseudo-Relativistic Non-Autonomous Schrödinger Equation

Sébastien Breteaux, Jérémy Faupin, Viviana Grasselli

We establish a maximal velocity bound for a pseudo-relativistic quantum particle in an external time-dependent potential. Our estimate shows that the probability for the particle,…

math.AP2024

On the number of bound states for fractional Schr{ö}dinger operators with critical and super-critical exponent

Sébastien Breteaux, Jérémy Faupin, Viviana Grasselli

We study the number $N_{< 0} (H_{s})$ of negative eigenvalues, counting multiplicities, of the fractional Schrödinger operator $H_{s} = (- Δ)^{s} - V (x)$ on $L^{2} (R^{d})$ , for any $d \geq 1$ …

math.SP2024

On the definition of zero resonances for the Schr{ö}dinger operator with optimal scaling potentials

Viviana Grasselli

We consider the Schr{ö}dinger operator -- $Δ$ + V on the Euclidean space with potential in the Lorentz space L^{n/2,1} and we find necessary and sufficient conditions for zero to be…