The noncommutative Wiener lemma, linear independence, and spectral properties of the algebra of time-frequency shift operators |
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| Authors: | Radu Balan |
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| Affiliation: | Siemens Corporate Research, 755 College Road East, Princeton, New Jersey 08540 |
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| Abstract: | ![]()
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  function. We also estimate the coefficient decay of the inverse of finite linear combinations of time-frequency shifts. |
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| Keywords: | Time-frequency shifts operator algebras Wiener lemma trace |
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