The noncommutative Wiener lemma, linear independence, and spectral properties of the algebra of time-frequency shift operators
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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 $L^2$ function. We also estimate the coefficient decay of the inverse of finite linear combinations of time-frequency shifts.References
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Additional Information
- Radu Balan
- Affiliation: Siemens Corporate Research, 755 College Road East, Princeton, New Jersey 08540
- Address at time of publication: Department of Mathematics, University of Maryland, College Park, Maryland 20742
- MR Author ID: 356464
- Email: radu.balan@siemens.com, rvbalan@math.umd.edu
- Received by editor(s): November 9, 2005
- Received by editor(s) in revised form: October 3, 2006
- Published electronically: January 11, 2008
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 3921-3941
- MSC (2000): Primary 43A20; Secondary 42C15, 46H30
- DOI: https://doi.org/10.1090/S0002-9947-08-04448-6
- MathSciNet review: 2386252