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Analysis and Geometry on Groups : Cambridge Tracts in Mathematics - Nicholas Theodoros Varopoulos

Analysis and Geometry on Groups

Cambridge Tracts in Mathematics

Hardcover

Published: 15th February 2003
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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 are not concerned 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 center this book around Lie groups, but could easily have pushed it in several other directions as it interacts with the theory of second order partial differential operators, and probability theory, as well as with group theory.

"The book is very concise and contains a great wealth of ideas and results...Each chapter contains a small section, 'References and comments', in which the authors, in their own way, introduce the reader to the brief history of the subject and its bibliography." A. Hulanicki, Mathematical Reviews

Preface
Foreword
Introduction
Dimensional inequalities for semigroups of operators on the Lp spaces
Systems of vector fields satisfying Hörmander's condition
The heat kernel on nilpotent Lie groups
Local theory for sums of squares of vector fields
Convolution powers on finitely generated groups
Convolution powers on unimodular compactly generated groups
The heat kernel on unimodular Lie groups
Sobolev inequalities on non-unimodular Lie groups
Geometric applications
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521353823
ISBN-10: 0521353823
Series: Cambridge Tracts in Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 172
Published: 15th February 2003
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.8 x 15.2  x 1.4
Weight (kg): 0.43