Piero D’Ancona

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20242026

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math.AP2025

A dynamical Amrein-Berthier uncertainty principle

Piero D'Ancona, Diego Fiorletta

Given a selfadjoint magnetic Schrödinger operator \begin{equation*} H = ( i \partial + A(x) )^2 + V(x) \end{equation*} on $L^{2} (R^{n})$ , with $V (x)$ strictly subquadratic a…

math.AP2025

Uniform resolvent estimates for magnetic operators

Piero D'Ancona, Zhiqing Yin

We prove Kenig--Ruiz--Sogge type uniform resolvent estimates for selfadjoint magnetic Schrödinger operators $H = (i \partial + A (x))^{2} + V (x)$ on $R^{n}$ , $n \geq 3$ . Under suitable…

math.AP2025

Dispersive and Strichartz estimates for Dirac equation in a cosmic string spacetime

Piero D'Ancona, Zhiqing Yin, Junyong Zhang

In this work we study the Dirac equation on the cosmic string background, which models a one--dimensional topological defect in the spacetime. We first define the Dirac operator in…