Wiener's lemma for twisted convolution and Gabor frames

By Karlheinz Gröchenig, M. Leinert. 2003

251 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/2391c517a8a6f47a0d537aed2bb6d18c6c8ffff9

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In Applied Mathematics

Citations in the corpus

Modulation Spaces: Looking Back and Ahead (2006, methodology): “[122], the rational case was done by different methods in [78]).”
Approximation of the Fourier Transform and the Dual Gabor Window (2005, unknown): “Lemma 6 ([19, 29]).”
Weight Functions in Time-Frequency Analysis (2006, background): “In [19] only radial weight functions were considered; the general case can be deduced from the general Theorem 6.”
Density, Overcompleteness, and Localization of Frames. II. Gabor Systems (2005, background): “This greatly extends a recent result of Gr¨ochenig and Leinert [GL04] which covered only the case of lattice Gabor frames.”
Time-Frequency Analysis of Sj\"ostrand's Class (2004, background): “ergence can be extended to other function spaces. The following theorem summarizes the main properties of Gabor expansions and the characterization of time-frequency behavior by means of Gabor frames [17,26] Theorem 2.2. Let v be an admissible weight function (in particular v satisﬁes the GRS-condit”
Wiener algebras of Fourier integral operators (2013, background): “The time–frequency analysis of pseudodifferential operators was propagated in [20,22,23,27,34].”
Banach Gelfand Triples for Gabor Analysis (2008, methodology): “Later we will return to this topic in the context of Gröchenig/Leinert’s resolution of the ”irrational case”-conjecture [30].”
Dynamical Sampling and Systems from Iterative Actions of Operators (2016, background): “The dynamical sampling problem has connections and applications to other areas of mathematics including, Banach algebras, C∗-algebras, spectral theory of normal operators, and frame theory [2, 8, 10, 13, 14, 15, 26, 32].”
Finite Discrete Gabor Analysis (2007, unknown): “In [31, 43] it is shown that if g ∈ S0(R) then also γ ∈ S0 (R).”
Convergence Analysis of the Finite Section Method and Banach Algebras of Matrices (2010, methodology): “The algebra A1v was treated by one of us with Leinert [13].”
Wiener's lemma for infinite matrices with polynomial off-diagonal decay (2005, background): “, des termes llows: rtant and 4], time- In this Note, we give a simple elementary proof to Wiener’s lemma for infinite matrices with polynomial off-diagonal”
Time-Frequency Analysis of Sjöstrand's Class (2004, background): “The following theorem summarizes the main properties of Gabor expansions and the characterization of time-frequency behavior by means of Gabor frames [17,26]”
Symmetry and inverse-closedness of matrix algebras and functional calculus for infinite matrices (2006, methodology): “This statement has been instrumental for the construction of Gabor frames with good time-frequency concentration and the solution of a conjecture of Janssen and Feichtinger [20].”
Localization of Frames, Banach Frames, and the Invertibility of the Frame Operator (2004, methodology): “For uniform Gabor frames, such results have already been obtained by means of fairly deep methods from the theory of Banach algebras [ 35 , 33].”