The Weyl calculus
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We start with a description of the basic features of the Weyl pseudo-differential analysis, to be used throughout the book: the emphasis is on group-theoretic properties, which is what is needed in the sequel. In the first section of the chapter, we shall show in which way the analysis of operators from the Weyl calculus by means of their diagonal matrix elements against appropriate families, parametrized by points of the hyperbolic half-plane II, of functions of Gaussian type, establishes a link between function theory on the plane and on the hyperbolic half-plane.
KeywordsModular Form Wigner Function Integral Kernel Symbolic Calculus Composition Formula
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