Lie theory ; Vol.230 : Harmonic analysis on symmetric spaces, general Plancherel theorems
- Author
- Jean-Philippe Anker, Bent Orsted
- Publication Year
- 2005
- Publisher
- Springer
- Language
- English
- Document Type
- Book
- Faculty / Subject Heading
- Mathematics and Statistics
- Download Book Read book
Van den Ban’s introductory chapter explains the basic setup of a reductive symmetric space along with a careful study of the structure theory, particularly for the ring of invariant differential operators for the relevant class of parabolic subgroups. Advanced topics for the formulation and understanding of the proof are covered, including Eisenstein integrals, regularity theorems, Maass–Selberg relations, and residue calculus for root systems. Schlichtkrull provides a cogent account of the basic ingredients in the harmonic analysis on a symmetric space through the explanation and definition of the Paley–Wiener theorem. Approaching the Plancherel theorem through an alternative viewpoint, the Schwartz space, Delorme bases his discussion and proof on asymptotic expansions of eigenfunctions and the theory of intertwining integrals.
Keywords: Mathematics and Statistics / Algebra / Harmonic analysis / Lie group / Representation theory
