ALBERTI , Giovanni

We prove global Hölder regularity for the solutions to the time-harmonic anisotropic Maxwell's equations, under the assumptions of Hölder continuous coefficients. The regularity hypotheses on the coefficients are minimal. The same estimates hold also in the case of bianisotropic material parameters.

We consider a compressed sensing problem in which both the measurement and the sparsifying systems are assumed to be frames (not necessarily tight) of the underlying Hilbert space of signals, which may be finite or infinite dimensional. The main result gives explicit bounds on the number of measurements in order to achieve stable recovery,...

In this paper we introduce the randomised stability constant for abstract inverse problems, as a generalisation of the randomised observability constant, which was studied in the context of observability inequalities for the linear wave equation. We study the main properties of the randomised stability constant and discuss the implications for...

We consider the dynamical superresolution problem consisting in the recovery of positions and velocities of moving particles from low-frequency static measurements taken over multiple time steps. The standard approach to this issue is a two-step process: first, at each time step some static reconstruction method is applied to locate the...

We study the essential spectrum of operator pencils associated with anisotropic Maxwell equations, with permittivity ε, permeability μ and conductivity σ, on finitely connected unbounded domains. The main result is that the essential spectrum of the Maxwell pencil is the union of two sets: namely, the spectrum of the pencil div((ωε+iσ)∇·), and...