The Noncommutative Wiener Lemma, Linear Independence, and Spectral Properties of the Algebra of Time-frequency Shift Operators
نویسنده
چکیده
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 L2 function. We also estimate the coefficient decay of the inverse of finite linear combinations of time-frequency shifts.
منابع مشابه
A Noncommutative Wiener Lemma and A Faithful Tracial State on Banach Algebras of Time–Frequency Shift Operators
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 implies the algebra contains no compact operators. As a corollary we obtain a special case of the Heil-Ramanathan-Topiwala conjecture regarding linear independence of ...
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