Time-Frequency Analysis of Sjöstrand's Class

By Karlheinz Gröchenig. 2004

188 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Signal Processing

View Paper: https://www.semanticscholar.org/paper/59ea880da6f56c45be0dda6a5661ec0eeeac3fa3

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Citations in the corpus

Modulation Spaces: Looking Back and Ahead (2006, unknown): “also [116, 125].”
Weight Functions in Time-Frequency Analysis (2006, background): “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].”
The dilation property of modulation spaces and their inclusion relation with Besov spaces (2006, background): “Nowadays Sjöstrand’s symbol class is recognized as a special case of the modulation spaces by Gröchenig [5].”
The Mystery of Gabor Frames (2014, methodology): “Gabor frames are used as a tool for the characterization of smoothness properties and phase space concentration [25,30,36], for the study of pseudodifferential operators [37] and, of course, in signal processing [30,31].”
Weight Functions in Time-Frequency Analysis (2006, background): “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].”
Convergence Analysis of the Finite Section Method and Banach Algebras of Matrices (2010, background): “This type of “convolution-dominated” decay of matrices plays an important role in the discretization of pseudodifferential operators with respect to Gabor frames [12, 15] and in mobile communications [28].”
Stability of Localized Operators (2008, methodology): “For example, the classical Wiener’s lemma and its weighted variation ([39]) were used to establish the decay property at infinity for dual generators of a shift-invariant space ([1,43]); the Wiener’s lemma for matrices associated with twisted convolution was used in the study the decay properties of”
Unimodular Fourier multipliers for modulation spaces (2006, background): “Their many applications are surveyed in [7]; for the special case of M∞,1, which is sometimes called the Sjöstrand class, see also [12,13,21,28] and the references therein.”
Banach algebras of pseudodifferential operators and their almost diagonalization (2007, methodology): “The next lemma taken from [27] explains the additional properties of M(σ).”
The inclusion relation between Sobolev and modulation spaces (2010, background): “Because of this special nature, modulation spaces are now considered to be suitable spaces in the analysis of pseudo-differential operators after a series of important works [3], [7], [8], [9], [17], [18] and so on.”
Wiener’s Lemma for Infinite Matrices II (2007, background): “The inverse-closed property for non-commutative matrix subalgebra has been shown to be crucial for the well-localization of dual wavelet frames and dual Gabor frames [4, 24, 29, 30, 31], the algebra of pseudodifferential operators [22, 28, 39], the fast implementation in numerical analysis [12, 13, ”
Pseudodifferential operators on locally compact abelian groups and Sjöstrand's symbol class (2006, methodology): “Analogous to [19] we define the modulation space M m (G) as the completion of the space SC(G) with respect to the M m -norm, when p, q < ∞ and the weak∗completion if pq = ∞.”