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Weyl Transforms
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The roles of the Heisenberg group and the symplectic group in the study of the structure of the Weyl transform are explicated, and the connections of the Weyl transform with quantization are highlighted throughout the book. Localization operators, first studied as filters in signal analysis, are shown to be Weyl transforms with symbols expressed in terms of the admissible wavelets of the localization operators. The results and methods in this book should be of interest to graduate students and mathematicians working in Fourier analysis, operator theory, pseudo- differential operators and mathematical physics. Background materials are given in adequate detail to enable a graduate student to proceed rapidly from the very basics to the frontier of research in an area of operator theory.
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