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001 u377027
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007 cr nn 008mamaa
008 110728s2011 sz | s |||| 0|eng d
020 _a9783764399924
_9978-3-7643-9992-4
040 _cMX-MeUAM
050 4 _aQA329-329.9
082 0 4 _a515.724
_223
100 1 _aGosson, Maurice A.
_eauthor.
245 1 0 _aSymplectic Methods in Harmonic Analysis and in Mathematical Physics
_h[recurso electrónico] /
_cby Maurice A. Gosson.
264 1 _aBasel :
_bSpringer Basel,
_c2011.
300 _aXXIV, 338p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aPseudo-Differential Operators, Theory and Applications ;
_v7
520 _aThe 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 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 pseudo-differential 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 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.
650 0 _aMathematics.
650 0 _aOperator theory.
650 0 _aDifferential equations, partial.
650 0 _aGlobal differential geometry.
650 1 4 _aMathematics.
650 2 4 _aOperator Theory.
650 2 4 _aPartial Differential Equations.
650 2 4 _aMathematical Physics.
650 2 4 _aDifferential Geometry.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783764399917
830 0 _aPseudo-Differential Operators, Theory and Applications ;
_v7
856 4 0 _zLibro electrónico
_uhttp://148.231.10.114:2048/login?url=http://link.springer.com/book/10.1007/978-3-7643-9992-4
596 _a19
942 _cLIBRO_ELEC
999 _c204907
_d204907