# Analysis Seminar on "Spatio-spectral limiting on Boolean cubes" by Joe Lakey (NMSU)

### Event Description:

**Title: **Spatio-spectral limiting on Boolean cubes

**Abstract:** Boolean cubes are just Nth powers of the integers mod 2, thought of as graphs.

The composition of an operator that truncates to an interval around the origin and then to low frequencies was studied, on the real line, in the 1960s by mathematicians at Bell Labs. Its eigenvectors are so-called prolate spheroidal wave functions and its eigenvalues, remarkably, are close to one up to a parameter known as the time--bandwidth product, then decay rapidly to zero. Analogues of these operators were studied in finite and discrete settings, thought of as approximations of the continuous setting, and in Euclidean space, where eigenvalue decay is less remarkable.

Here we study instead what happens in higher dimensions of a very discrete setting: the integers mod 2. Specifically, we define and characterize eigenspaces of an analogue of the time- and band-limiting operator on Boolean cubes and outline techniques to compute these objects. Extensions to some other special graphs are also considered.

About the Speaker: Joe Lakey