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The noncommutative Wiener lemma, linear independence, and spectral properties of the algebra of time-frequency shift operators
Transactions of the American Mathematical Society
In this paper we analyze the Banach *-algebra of time-frequency shifts with absolutely summable coefficients. We prove a noncommutative version of the Wiener lemma. We also construct a faithful tracial state on this algebra which proves the algebra contains no compact 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. We also estimate the coefficient decay of thedoi:10.1090/s0002-9947-08-04448-6 fatcat:ji2akznl3rhuhflfgpwrtfoti4