Information-Completeness and Shannon Sampling with Ambiguities

Vortrag von Dr. Lukas Liehr

Datum: 08.10.25  Zeit: 16.30 - 18.00  Raum: ETH HG G 19.2

Are two functions identical if they take the same values on discrete samples? According to classical Shannon sampling, the answer to this type of uniqueness question is yes when the functions are band-limited. In fact, the uniqueness question is determined by the density of the discrete samples. We study non-linear versions of this problem, where it is assumed that the functions agree only up to multiplicative symmetries. We develop a non-linear Shannon-type theory, obtaining sharp results that characterize when uniqueness holds and when it fails. In special cases, this framework recovers results from phase retrieval. Finally, we investigate the problem in finite dimensions, where it is related to information-completeness in quantum theory. In this setting, we demonstrate that the problem exhibits behavior markedly different from the infinite-dimensional case of band-limited functions. The talk is based on joint work with Tomasz Szczepanski (University of Alberta).