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ISSN 1088-6850(e) ISSN 0002-9947(p)

The noncommutative Wiener lemma, linear independence, and spectral properties of the algebra of time-frequency shift operators

Author(s): Radu Balan
Journal: Trans. Amer. Math. Soc. 360 (2008), 3921-3941.
MSC (2000): Primary 43A20; Secondary 42C15, 46H30
Posted: January 11, 2008
MathSciNet review: 2386252
Retrieve article in: PDF

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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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