Coherent States, Wavelets, and Their Generalizations by Syed Twareque Ali Jean-Pierre Antoine & Jean-Pierre Gazeau

Author:Syed Twareque Ali, Jean-Pierre Antoine & Jean-Pierre Gazeau
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

This definition is reasonable insofar as differentiability properties of (11.66) are those of the displacement operator D(z). We will extend this definition to distributions in the next subsection. In the CS case, the fact that the Berezin transform is a Gaussian convolution is of great importance. It explains the robustness of CS quantization, since it is well defined for a very large class of non smooth functions and even, as will be shown below, for a class of distributions including the tempered ones.

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