Composition and spectral invariance of pseudodifferential Operators on Modulation Spaces

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Banach algebras of pseudodifferential operators and their almost diagonalization (2007, methodology): “Independently, an alternative approach with time-frequency methods was developed in [28, 29, 24, 26 , 27].”
Weyl product algebras and modulation spaces (2007, methodology): “Later on Gröchenig extended in [12] the Wiener property to modulation spaces of the form M∞,1 (ω) (R2d), where ω(X,Y )= ω(Y ) is submultiplicative and satisfies some appropriate conditions.”
Weight Functions in Time-Frequency Analysis (2006, methodology): “The following theorem was proved in [40] for the unweighted case v ≡ 1, a different proof was given in [42], weighted versions and two genuine time-frequency proofs were obtained in [17, 18] (for the Weyl calculus), the extension to LCA groups is contained in [23].”
Weight Functions in Time-Frequency Analysis (2006, methodology): “The following theorem was proved in [40] for the unweighted case v ≡ 1, a different proof was given in [42], weighted versions and two genuine time-frequency proofs were obtained in [17, 18] (for the Weyl calculus), the extension to LCA groups is contained in [23].”
Wiener algebras of Fourier integral operators (2013, background): “The time–frequency analysis of pseudodifferential operators was propagated in [20,22,23,27,34].”