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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Symplectic Methods in Harmonic Analysis and in Mathematical Physics

Symplectic Methods in Harmonic Analysis and in Mathematical Physics

de Gosson, Maurice A.

Paperback

Series: Pseudo-Differential Operators, Book 7

General MathematicsPhysics

ISBN10: 3764399910
ISBN13: 9783764399917
Publisher: Springer Nature
Published: Jul 30 2011
Pages: 338
Weight: 1.25
Height: 0.90 Width: 6.60 Depth: 9.40
Language: English

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, Shubin's global theory of pseudo-differential operators, and Feichtinger's 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 where the main role is played by Bopp operators (also called Landau operators in the literature) is introduced and studied. 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 Feichtinger's modulation spaces are key actors.

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