Time–Frequency analysis of localization operators

By Elena Cordero, Karlheinz Gröchenig. 2003

300 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b5fe2da0572afbddd014421144088e9391dca8e1

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In Applied Mathematics

In Computer Vision and Pattern Recognition

In Mathematical Physics

Citations in the corpus

Continuity Properties for Modulation Spaces, with Applications to Pseudo-Differential Calculus, II (2004, background): “Remark 4.14. In [ 5 ], Cordero and Grochenig present a converse of Corollary 4.12 in the case p = q =∞ and r1 = r2 = 1, and the weight functions satisfy some extra conditions (cf.”
Fourier multipliers of classical modulation spaces (2006, background): “See [2,14,23,24] for this kind of applications.”
Time-Frequency Analysis of Sjöstrand's Class (2004, background): “This line of investigation and the emphasis on time-frequency techniques was continued in [11] [12] [23] [24] [31] [32].”
Composition and spectral invariance of pseudodifferential Operators on Modulation Spaces (2006, background): “…analysis, specifically time-frequency analysis, general modulation spaces have been introduced as symbol classes and in some cases modulation spaces have been shown to yield detailed classifications of the boundedness [18] [19] and optimal results for phase-space-localization operators [5] [6].”
MODULATION SPACES AND A CLASS OF BOUNDED MULTILINEAR PSEUDODIFFERENTIAL OPERATORS (2005, methodology): “Further developments using modulation spaces have since been obtained in [5], [15], [18], [21], [22], [25].”
Micro-Local Analysis with Fourier Lebesgue Spaces. Part I (2011, background): “If in addition f has compact support, then the following estimate holds (see Proposition 3.6 in [ 3 ]).”
Time-Frequency Analysis of Sj\"ostrand's Class (2004, methodology): “as symbol classes for pseudodiﬀerential operators were introduced in [23] independently of Sj¨ostrand’s work. This line of investigation and the emphasis on time-frequency techniques was continued in [11,12,23,24,31,32]. To make the connection to time-frequency analysis, we introduce the operators o”
Modulation Spaces: Looking Back and Ahead (2006, unknown): “[32] E.”
Unimodular Fourier multipliers for modulation spaces (2006, background): “However, to keep the presentation self-contained, we sketch a simple and direct proof that is based on the convolution relations in [4].”
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.”