Modulation Spaces: Looking Back and Ahead

By Hans G. Feichtinger. 2006

242 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/6ec223243335fcaef9757f05bfcd213388c732af

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Projective modules over noncommutative tori are multi-window Gabor frames for modulation spaces (2008, methodology): “Modulation spaces have found many applications in harmonic analysis and time-frequency analysis, see the interesting survey article [15] for an extensive bibliography.”
Micro-Local Analysis with Fourier Lebesgue Spaces. Part I (2011, background): “We refer to [ 6 ] for the most updated definition of modulation spaces.”
Changes of variables in modulation and Wiener amalgam spaces (2008, background): “(We refer to [12] for the most updated definition of modulation spaces.”
The Mystery of Gabor Frames (2014, background): “See [22] for the original publication on modulation spaces, [23] for a historical survey, and [36] for a systematic introduction.”
Fourier multipliers of classical modulation spaces (2006, methodology): “The “continuous” definition uses the “short-time Fourier transform” as mentioned in the Introduction [10,11].”
Unimodular Fourier multipliers for modulation spaces (2006, background): “Little is known for α ∈ (0,1), and many results are concerned almost exclusively with appropriate corrections of the symbol ei|ξ |α with functions that are essentially smooth away from the origin [14, 20,29].”
History and Evolution of the Density Theorem for Gabor Frames (2007, background): “For an interesting personal historical account of the development of the modulation spaces, including the Feichtinger algebra in particular, see Feichtinger’s recent article [63].”