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.
