Kasso Okoudjou

Time frequency analysis seeks to study functions or signals in both space and frequency. In this talk I will focus on one time-frequency tool: the Weyl-Heisenberg or Gabor systems. The origin of these systems can be partially attributed to Dennis Gabor, who, in 1946, claimed that any square Lebesgue integrable function can be written as an infinite linear combination of time and frequency shifts of the standard Gaussian. Since then, decomposition methods for larger classes of functions or distributions in terms of various elementary building blocs have lead to an impressive body of work in harmonic analysis. In this talk, I will give a brief introduction to the theory of Gabor frames and will survey some related easily stated yet unresolved open problems.