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Analysis and Geometry on Groups

Analysis and Geometry on Groups by Nicholas T. Varopoulos
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The geometry and analysis that is discussed in this book extends to classical results for general discrete or Lie groups, and the methods used are analytical but have little to do with what is described these days as real analysis. Most of the results described in this book have a dual formulation; they have a 'discrete version' related to a finitely generated discrete group, and a continuous version related to a Lie group. The authors chose to centre this book around Lie groups but could quite easily have pushed it in several other directions as it interacts with opetators, and probability theory, as well as with group theory. This book will serve as an excellent basis for graduate courses in Lie groups, Markov chains or potential theory.
Cambridge University Press; January 1993
170 pages; ISBN 9780511829437
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Title: Analysis and Geometry on Groups
Author: Nicholas T. Varopoulos; L. Saloff-Coste; T. Coulhon