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Field name	Details
Dewey Class	515.2433
Title	Symplectic Methods in Harmonic Analysis and in Mathematical Physics ([Ebook]) / by Maurice A. Gosson.
Author	Gosson, Maurice A.
Other name(s)	SpringerLink (Online service)
Publication	Basel : Springer , 2011.
Physical Details	XXIV, 338 pages : online resource.
Series	Pseudo-Differential Operators, Theory and Applications ; 7
ISBN	9783764399924
Summary Note	The aim of this book is to give a rigorous and complete treatment of various topics from harmonic analysis with a strong emphasis on symplectic invariance properties, which are often ignored or underestimated in the time-frequency literature. The topics that are addressed include (but are not limited to) the theory of the Wigner transform, the uncertainty principle (from the point of view of symplectic topology), Weyl calculus and its symplectic covariance, Shubinâs global theory of pseudo-differential operators, and Feichtingerâs theory of modulation spaces. Several applications to time-frequency analysis and quantum mechanics are given, many of them concurrent with ongoing research. For instance, a non-standard pseudo-differential calculus on phase space is introduced and studied, where the main role is played by âBopp operatorsâ (also called âLandau operatorsâ in the literature). This calculus is closely related to both the Landau problem and to the deformation quantization theory of Flato and Sternheimer, of which it gives a simple pseudo-differential formulation where Feichtingerâs modulation spaces are key actors. This book is primarily directed towards students or researchers in harmonic analysis (in the broad sense) and towards mathematical physicists working in quantum mechanics. It can also be read with profit by researchers in time-frequency analysis, providing a valuable complement to the existing literature on the topic. A certain familiarity with Fourier analysis (in the broad sense) and introductory functional analysis (e.g. the elementary theory of distributions) is assumed. Otherwise, the book is largely self-contained and includes an extensive list of references.:
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-3-7643-9992-4
Links to Related Works	Subject References: Differential equations, Partial . Differential Geometry . Global differential geometry . Harmonic analysis . Mathematical Physics . Operator Theory . Symplectic geometry . Authors: Gosson, Maurice A. . Corporate Authors: SpringerLink (Online service) . Series: Pseudo-Differential Operators, Theory and Applications . Classification: 515.2433 . 515.2433 (DDC 23) .

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Symplectic Methods in Harmonic Analysis and in Mathematical Physics

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