A famous theorem of Wiener states that if a periodic function has an absolutely convergent Fourier series and never vanishes, then its reciprocal also has an absolutely convergent Fourier series. In a forthcoming paper by K. Grochenig and M. Leinert (Journal of the American Mathematical Society), this is generalized, using the techniques of abstract harmonic analysis to a noncommutative setting, and then applied to the theory of Gabor frames in time-frequency analysis. In this talk,
I'll present their proof of the generalization. Future talks will be devoted to the applications mentioned above.