Pseudo-Differential Operators and Symmetries Background Analysis and Advanced Topics /

• Main Authors: Ruzhansky, Michael. (Author), Turunen, Ville. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Basel : Birkhũser Basel, 2010.
• Series: Pseudo-Differential Operators, Theory and Applications ; 2
• Subjects: Mathematics.; Topological Groups.; Global analysis.; Differential equations, partial.; Partial Differential Equations.; Topological Groups, Lie Groups.; Global Analysis and Analysis on Manifolds.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-7643-8514-9

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 par...

Table of Contents:

• 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.