An almost periodic noncommutative Wiener's Lemma (Q984786)

Wiener's Tauberian Lemma states that if a periodic function \(f\) has an absolutely convergent Fourier series and never vanishes, then \(1/f\) also has an absolutely convergent Fourier series. The authors develop a theory of almost periodic elements in Banach algebras and present an abstract version of a noncommutative Wiener's Lemma. The theory can be used to derive some recent results in time frequency analysis, such as the spectral properties of the finite linear combinations of time-frequency shifts.