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 necessary or sufficient conditions for such reconstruction in terms of an adequate notion of density of the set of samples. The most classical density theorems, due to Shannon and Beurling, involve bandlimited functions (that is, functions whose Fourier transforms are supported on the unit interval) and provide a precise geometric characterization of all configurations of points that lead to reconstruction. I will present modern variants of these results and their implications in the field to time-frequency analysis, notably in the construction of functional expansions consisting of time-frequency shifts of a given profile function (known as Gabor or Weyl-Heisenberg systems).
Density theorems for sampling and time-frequency analysis
19.06.2020 14:20 - 15:05
Organiser:
Fakultät für Mathematik
Location:
Zoom Meeting