Boundedness and Compactness of Localization Operators Associated with the Spherical Mean Wigner Transform

2018 ◽  
Vol 13 (3) ◽  
pp. 753-780
Author(s):  
Hatem Mejjaoli ◽  
Khalifa Trimèche
Keyword(s):  
Wigner Transform ◽  
Localization Operators ◽  
Spherical Mean

Localization operators, time frequency concentration and quantitative-type uncertainty for the continuous wavelet transform associated with spherical mean operator

2019 ◽  
Vol 17 (04) ◽  
pp. 1950022 ◽  
Author(s):  
Hatem Mejjaoli ◽  
Nadia Ben Hamadi ◽  
Slim Omri
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Finite Measure ◽  
Continuous Wavelet ◽  
Uncertainty Principles ◽  
Localization Operators ◽  
Spherical Mean Operator ◽  
Von Neumann ◽  
Time Frequency ◽  
Spherical Mean

We consider the continuous wavelet transform [Formula: see text] associated with the spherical mean operator. We investigate the localization operators for [Formula: see text], in particular, we prove that they are in the Schatten-von Neumann class. Next, we analyze the concentration of this transform on sets of finite measure. In particular, Donoho-Stark and Benedicks-type uncertainty principles are given. Finally, we prove many versions of quantitative uncertainty principles for [Formula: see text].

THE DME AS AN APPROXIMATION TO THE WIGNER TRANSFORM

1984 ◽  
Vol 45 (C6) ◽  
pp. C6-199-C6-204
Author(s):  
J. Martorell ◽  
E. Moya de Guerra
Keyword(s):  
Wigner Transform
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