Lie Theory: Harmonic Analysis on Symmetric Spaces - General Plancherel Theorems

by Jean-Philippe Anker (Editor), Bent Orsted (Editor)

Overview

Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics. Three independent, self-contained volumes, under the general title of Lie Theory, feature survey work and original results by well-established researchers in key areas of semisimple Lie theory.

Harmonic Analysis on Symmetric Spaces – General Plancherel Theorems presents extensive surveys by E.P. van den Ban, H. Schlichtkrull, and P. Delorme of the spectacular progress over the past decade in deriving the Plancherel theorem on reductive symmetric spaces. Well suited for both graduate students and researchers in semisimple Lie theory and neighboring fields, possibly even mathematical cosmology, it provides a broad, clearly focused examination of semisimple Lie groups and their integral importance and applications to research in many branches of mathematics and physics. Knowledge of basic representation theory of Lie groups as well as familiarity with semisimple Lie groups, symmetric spaces, and parabolic subgroups is required.

Product Details

ISBN-13:	9780817637774
Publisher:	Birkhäuser Boston
Publication date:	01/04/2005
Series:	Progress in Mathematics , #230
Edition description:	2005
Pages:	175
Product dimensions:	6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

The Plancherel Theorem for a Reductive Symmetric Space.- The Paley—Wiener Theorem for a Reductive Symmetric Space.- The Plancherel Formula on Reductive Symmetric Spaces from the Point of View of the Schwartz Space.

Editorial Reviews

"This book is a remarkable and highly commendable effort by three leading experts, Erik P. van den Ban, Henrik Schlichtkrull, and Patrick Delorme, to survey the fascinating progress made in the last decade on the Plancherel theorem for reductive symmetric spaces." —-Mathematical Reviews

"Well suited for both graduate students and researchers in semisimple Lie theory and neighbouring fields, and possibly even mathematical cosmology, Harmonic Analysis on Symmetric Spaces - General Plancherel Theorems provides a broad, clearly focused examination of semisimple Lie groups and their integral importance and applications to research in many braches of mathematics and physics." —-L'Enseignement Mathématique

From the Publisher