UBC Math Department Colloquium: Alex Iosevich

A classical problem in signal recovery is to determine whether a finite signal can be recovered from its Fourier transform with missing values. This problem has been studied by many authors starting with the seminal papers by Matolsci and Szuks in the 70s and Donoho and Stark in the late 80s. The general theme is that the recovery is possible if the set of missing values is not too large and the signal is sufficiently sparse. Azita Mayeli and I showed a couple of years ago that recovery condition improves significantly if the set of missing values satisfies a non-trivial Fourier restriction estimate. We shall discuss these and related results, as well as the role of the classical Lambda(p) inequality due to Bourgain in this theory. We will also show how these types of results can be applied to the study of missing values in time series in data science.