F. Alberto Grunbaum (Biography)
Department of Mathematics
UC Berkeley
USA

“The Problem of 'Simultaneous Concentration' in Physical and Frequency Space: The Cases of the Fourier Transform, the Fourier Series and the DFT”

Abstract

Many applications involve reconstructing a function from (maybe partial) knowledge of its Fourier transform. In certain cases the correct mathematical model is that of the real line or a higher dimensional euclidean space, in others it is a lattice. In real life computations one needs to change both of these infinite models by that of the N roots of unity and deal with the DFT. I will discuss some of the pitfalls in this area with particular emphasis on the problem of double concentration at the root of the work of W.Heisenberg, C.Shannon and many others.