Time-Frequency Shift Operators

Wednesday, Sept 28, 2005, 2-3:00pm, WWH 1314

In this talk I analyze the Banach *-algebra of arbitrary time-frequency shifts with absolute summable coefficients. In this context I present a noncommutative version of the Wiener lemma, by which an operator of this algebra that is invertible in B(L^2) has the inverse again in this algebra. I also construct a faithful trace that allows to prove such algebras are free of Hilbert-Schmidt operators. As a corollary we obtain a special case of the Heil-Ramanathan-Topiwala conjecture regarding linear independence of finitely many time-frequency shifts of one L^2 function.