Modulation Spaces on Locally Compact Abelian Groups

By Hans G. Feichtinger. 2003

706 citations recorded by the source corpus.

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Citations in the corpus

On anisotropic Triebel-Lizorkin type spaces, with applications to the study of pseudo-differential operators (2008, background): “Feichtinger introduced the family of modulation spaces [14] which correspond to a uniform decomposition of frequency space.”
Generalized coorbit space theory and inhomogeneous function spaces of Besov-Lizorkin-Triebel type (2010, methodology): “Also modulation spaces and characterizations via Gabor frames [29, 18], Bergman spaces [20], and the more recent shearlet spaces [13] can be treated via classical coorbit space theory.”
Time-Frequency Analysis of Sj\"ostrand's Class (2004, methodology): “ q = ∞, we use a weak-∗ completion. For p = q we write Mp m for M p,p m , for m ≡ 1, we write Mp,q instead of Mp,q m . For the theory of modulation spaces and some applications we refer the reader to [16] and [21, Ch. 11-13] REMARKS: 1. The cautionary deﬁnition is necessary only for weights of super”
Banach algebras of pseudodifferential operators and their almost diagonalization (2007, background): “he starting point of the time-frequency approach is the observation that the Sj¨ostrand class coincides with one of the so-called modulation spaces that were introduced by Feichtinger already in 1983 [17]. The time-frequency approach added several new insights and generalizations to pseudodiﬀerentia”
Modulation Spaces: Looking Back and Ahead (2006, background): “The original report [59] described most of those properties in the context of locally compact Abelian groups, because they are the natural context for these kind of function spaces (much in the same way that LCA groups are the natural context for harmonic analysis as such, according to André Weil, s”
Fourier multipliers of classical modulation spaces (2006, methodology): “The proofs can be found in [7,8,10].”
Frame Decomposition of Decomposition Spaces (2007, methodology): “The smoothness spaces considered here are special cases of a very general construction of decomposition spaces introduced by Feichtinger and Gröbner [19] and Feichtinger [16].”
On the global boundedness of Fourier integral operators (2008, methodology): “We briefly recall the definition of the modulation spaces M, 1 ≤ p ≤ ∞, which are widely used in time-frequency analysis (see [16, 22] and Section 2 for definition and properties).”
Wiener amalgam spaces for the fundamental identity of Gabor analysis (2005, methodology): “For our investigations we restrict our study to weighted mixed-norm spaces L m on R, [Fei83].”
WIENER RANDOMIZATION ON UNBOUNDED DOMAINS AND AN APPLICATION TO ALMOST SURE WELL-POSEDNESS OF NLS (2014, background): “The modulation spaces were introduced by Feichtinger [24] in early eighties.”
Pseudodifferential operators on ultra-modulation spaces (2004, background): “196 S. Pilipovii:, N. Teofanol' I Journal of Functional Analysis 208 (2004) 194-228 pseudodifferential operators.”
Sharpness of some properties of Wiener amalgam and modulation spaces (2008, unknown): “In fact, the space of admissible windows for the Wiener amalgam spaces W ( B , L q )( R d ) can be enlarged to the so-called Feichtinger algebra W Modulation spaces [10, 14].”
Continuity and Schatten Properties for Pseudo-differential Operators on Modulation Spaces (2006, methodology): “We refer to [ 15 ,20] for more facts about the W p,q (ω) -spaces.”
Projective modules over noncommutative tori are multi-window Gabor frames for modulation spaces (2008, background): “Modulation spaces [13] were introduced by Feichtinger in 1983.”