Symplectic Methods in Harmonic Analysis and in Mathematical by Maurice A. de Gosson

The target of this publication is to offer a rigorous and entire therapy of assorted themes from harmonic research with a robust emphasis on symplectic invariance homes, that are usually overlooked or underestimated within the time-frequency literature. the themes which are addressed contain (but are usually not restricted to) the speculation of the Wigner remodel, the uncertainty precept (from the perspective of symplectic topology), Weyl calculus and its symplectic covariance, Shubin’s international 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 learn. for example, a non-standard pseudo-differential calculus on part house the place the most position is performed by way of “Bopp operators” (also referred to as “Landau operators” within the literature) is brought and studied. This calculus is heavily relating to either the Landau challenge and to the deformation quantization thought of Flato and Sternheimer, of which it offers an easy pseudo-differential formula the place Feichtinger’s modulation areas are key actors.

This booklet is essentially directed in the direction of scholars or researchers in harmonic research (in the vast experience) and in the direction of mathematical physicists operating in quantum mechanics. it might probably even be learn with revenue by way of researchers in time-frequency research, offering a important supplement to the present literature at the topic.

A convinced familiarity with Fourier research (in the extensive experience) and introductory useful research (e.g. the undemanding idea of distributions) is believed. another way, the booklet is basically self-contained and comprises an in depth record of references.