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.
Nicholas T. Varopoulos
, L. Saloff-Coste
, T. Coulhon
Cambridge University Press
Country of Publication:
Series: Cambridge Tracts in Mathematics
11 December 2008
Professional and scholarly
Preface; Foreword; 1. Introduction; 2. Dimensional inequalities for semigroups of operators on the Lp spaces; 3. Systems of vector fields satisfying Hoermander's condition; 4. The heat kernel on nilpotent Lie groups; 5. Local theory for sums of squares of vector fields; 6. Convolution powers on finitely generated groups; 7. Convolution powers on unimodular compactly generated groups; 8. The heat kernel on unimodular Lie groups; 9. Sobolev inequalities on non-unimodular Lie groups; 10. Geometric applications; Bibliography; Index.
Reviews for Analysis and Geometry on Groups
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