By Maurice A. de Gosson

The target of this publication is to provide a rigorous and whole therapy of assorted issues from harmonic research with a powerful emphasis on symplectic invariance houses, that are usually overlooked or underestimated within the time-frequency literature. the themes which are addressed comprise (but usually are not restricted to) the idea of the Wigner remodel, the uncertainty precept (from the viewpoint of symplectic topology), Weyl calculus and its symplectic covariance, Shubin’s worldwide idea of pseudo-differential operators, and Feichtinger’s concept of modulation areas. a number of purposes to time-frequency research and quantum mechanics are given, a lot of them concurrent with ongoing examine. for example, a non-standard pseudo-differential calculus on part house is brought and studied, the place the most position is performed by means of “Bopp operators” (also referred to as “Landau operators” within the literature). This calculus is heavily on the topic of either the Landau challenge and to the deformation quantization concept of Flato and Sternheimer, of which it offers an easy pseudo-differential formula the place Feichtinger’s modulation areas are key actors.

This ebook is essentially directed in the direction of scholars or researchers in harmonic research (in the huge feel) and in the direction of mathematical physicists operating in quantum mechanics. it may well even be learn with revenue by means of researchers in time-frequency research, offering a useful supplement to the prevailing literature at the subject. a undeniable familiarity with Fourier research (in the wide experience) and introductory useful research (e.g. the effortless concept of distributions) is thought. another way, the ebook is basically self-contained and comprises an in depth checklist of references.