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About Pseudo-Differential Operators and Symmetries: Background Analysis and Advanced Topics
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.
Detailed Information
| Author: | Michael Ruzhansky, Ville Turunen |
|---|---|
| Publication Year: | 2009 |
| ISBN: | 9783764385132 |
| Pages: | 712 |
| Language: | English |
| File Size: | 3.458 |
| Format: | |
| Price: | FREE |
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