Talk
Sampling, density, and equidistribution
Talk by Jose Luis Romero
Date: 24.02.21 Time: 16.15 - 17.45 Room: Online ZHACM
The sampling problem concerns the reconstruction of every function within a given class from their values observed only at certain points (samples). A density theorem gives precise necessary or sufficient conditions for such reconstruction in terms of an adequate notion of density of the set of samples. The most classical density theory, due to Shannon and Beurling, concerns bandlimited functions (that is, functions whose Fourier transforms are supported on the unit interval) and provides a sharp geometric characterization of all configurations of points that lead to stable reconstruction. I will present recent variants of such results and their applications in other fields, including the asymptotic equidistribution of Coulomb gases at low temperatures.