Symplectic Methods in Harmonic Analysis and in Mathematical Physics
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The work Symplectic Methods in Harmonic Analysis and in Mathematical Physics represents a distinct intellectual or artistic creation found in University of Manitoba Libraries. This resource is a combination of several types including: Work, Language Material, Books.
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Symplectic Methods in Harmonic Analysis and in Mathematical Physics
Resource Information
The work Symplectic Methods in Harmonic Analysis and in Mathematical Physics represents a distinct intellectual or artistic creation found in University of Manitoba Libraries. This resource is a combination of several types including: Work, Language Material, Books.
 Label
 Symplectic Methods in Harmonic Analysis and in Mathematical Physics
 Statement of responsibility
 by Maurice A. de Gosson
 Language

 eng
 eng
 Summary
 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 timefrequency 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 pseudodifferential operators, and Feichtinger’s theory of modulation spaces. Several applications to timefrequency analysis and quantum mechanics are given, many of them concurrent with ongoing research. For instance, a nonstandard pseudodifferential calculus on phase space is introduced and studied, where the main role is played by “Bopp operators” (also called “Landau operators” 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 pseudodifferential formulation where Feichtinger’s 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 timefrequency 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 selfcontained and includes an extensive list of references
 Dewey number
 530.12
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
 wn0UoTyER0
 Language note
 English
 LC call number
 QA329329.9
 Literary form
 non fiction
 Nature of contents
 dictionaries
 Series statement
 PseudoDifferential Operators, Theory and Applications,
 Series volume
 7
Context
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