Jubilee 2019

The Bell Labs theory of time and frequency limiting was developed primarily by Landau, Slepian and Pollak in the 1960s. It first identified the eigenfunctions of truncation in time followed by truncation in frequency, and subsequently described the distribution of eigenvalues of this composition of projections. An analogue of this theory is outlined in the setting of Boolean cubes, regarded as Cayley graphs of the N-th powers of the integers modulo two. This presentation focuses on eigenspaces of the spatial- and spectral-limiting analogues of the time- and frequency-limiting operators, emphasizing a technical apparatus in the Boolean setting that is substantially different from the case of the real line.