Continuity and Schatten-von Neumann properties for localization operators on modulation spaces. (English) Zbl 1342.47064
Summary: We use sharp convolution estimates for weighted Lebesgue and modulation spaces to obtain an extension of the celebrated Cordero-Gröchenig theorems on boundedness and Schatten-von Neumann properties of localization operators on modulation spaces. We also give a new proof of the Weyl connection based on the kernel theorem for Gelfand-Shilov spaces.
MSC:
| 47G30 | Pseudodifferential operators |
| 46F10 | Operations with distributions and generalized functions |
| 44A35 | Convolution as an integral transform |
Keywords:
localization operators; modulation space; short-time Fourier transform; Wigner transform; Schatten classCitations:
Zbl 1047.47038References:
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