Square-integrable group representations and localization operators for modified Stockwell transforms. (English) Zbl 1190.65205
The Stockwell transform and its modified version, a hybrid of the Gabor and the wavelet transform, using modulation, translation and dilation operations, fall into the class of square-integrable group representations. The resolution of the identity can then be used to introduce localization operators. First Schatten-von-Neumann classes and localization operators corresponding to square-integrable representations of locally compact and Hausdorff groups are recalled. The trace class norm inequalities for the trace class localization operators are studied and an explicit formula for the lower bound of the trace norm is given.
Reviewer: Kai Schneider (Marseille)
MSC:
65T60 | Numerical methods for wavelets |
65R10 | Numerical methods for integral transforms |
94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |
47G10 | Integral operators |
47G30 | Pseudodifferential operators |
43A32 | Other transforms and operators of Fourier type |