David Farahany, Department of Pure Mathematics, University of Waterloo
“Problems with inverting the Fourier transform”
A basic question in harmonic analysis is the following: given the Fourier transform of a function, how can one recover the original function? There are a number of ”natural” choices for how one may wish to do this. Interestingly, many of these techniques fail and whether some of these techniques succeed remains an open question. We’ll begin by defining the Fourier and inverse Fourier transforms, followed by some of their properties and limitations. Afterwards, we’ll give a survey of techniques for recovering a function from its Fourier transform. If time permits, we will also discuss relations to the Kakeya conjecture.