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100301s2010 sz | s |||| 0|eng d |
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|a 9783764385149
|9 978-3-7643-8514-9
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|a 10.1007/978-3-7643-8514-9
|2 doi
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|a QA370-380
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|a PBKJ
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|a MAT007000
|2 bisacsh
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|a 515.353
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|a Ruzhansky, Michael.
|e author.
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|a Pseudo-Differential Operators and Symmetries
|b Background Analysis and Advanced Topics /
|c by Michael Ruzhansky, Ville Turunen.
|h [electronic resource] :
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| 264 |
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|a Basel :
|b Birkhũser Basel,
|c 2010.
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| 300 |
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|b online resource.
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|a text
|b txt
|2 rdacontent
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|a computer
|b c
|2 rdamedia
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|a online resource
|b cr
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|a text file
|b PDF
|2 rda
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|a Pseudo-Differential Operators, Theory and Applications ;
|v 2
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|a Preface -- Introduction -- Part I Foundations of Analysis -- A Sets, Topology and Metrics -- B Elementary Functional Analysis -- C Measure Theory and Integration -- D Algebras -- Part II Commutative Symmetries -- 1 Fourier Analysis on Rn -- 2 Pseudo-differential Operators on Rn -- 3 Periodic and Discrete Analysis -- 4 Pseudo-differential Operators on Tn -- 5 Commutator Characterisation of Pseudo-differential Operators -- Part III Representation Theory of Compact Groups -- 6 Groups -- 7 Topological Groups -- 8 Linear Lie Groups -- 9 Hopf Algebras -- Part IV Non-commutative Symmetries -- 10 Pseudo-differential Operators on Compact Lie Groups -- 11 Fourier Analysis on SU(2) -- 12 Pseudo-differential Operators on SU(2) -- 13 Pseudo-differential Operators on Homogeneous Spaces -- Bibliography -- Notation -- Index.
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|a This monograph develops a global quantization theory of pseudo-differential operators on compact Lie groups. Traditionally, the theory of pseudo-differential operators was introduced in the Euclidean setting with the aim of tackling a number of important problems in analysis and in the theory of partial differential equations. This also yields a local theory of pseudo-differential operators on manifolds. The present book takes a different approach by using global symmetries of the space which are often available. First, a particular attention is paid to the theory of periodic operators, which are realized in the form of pseudo-differential and Fourier integral operators on the torus. Then, the cases of the unitary group SU(2) and the 3-sphere are analyzed in extensive detail. Finally, the monograph also develops elements of the theory of pseudo-differential operators on general compact Lie groups and homogeneous spaces. The exposition of the book is self-contained and provides the reader with the background material surrounding the theory and needed for working with pseudo-differential operators in different settings. The background section of the book may be used for independent learning of different aspects of analysis and is complemented by numerous examples and exercises.
|
| 650 |
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|a Mathematics.
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| 650 |
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|a Topological Groups.
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| 650 |
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|a Global analysis.
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| 650 |
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|a Differential equations, partial.
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| 650 |
1 |
4 |
|a Mathematics.
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| 650 |
2 |
4 |
|a Partial Differential Equations.
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| 650 |
2 |
4 |
|a Topological Groups, Lie Groups.
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| 650 |
2 |
4 |
|a Global Analysis and Analysis on Manifolds.
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| 700 |
1 |
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|a Turunen, Ville.
|e author.
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| 710 |
2 |
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|a SpringerLink (Online service)
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| 773 |
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|t Springer eBooks
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| 776 |
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8 |
|i Printed edition:
|z 9783764385132
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| 830 |
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|a Pseudo-Differential Operators, Theory and Applications ;
|v 2
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| 856 |
4 |
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|u https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-7643-8514-9
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| 912 |
# |
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|a ZDB-2-SMA
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| 950 |
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|a Mathematics and Statistics (Springer-11649)
|