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Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces

Lecture Notes from a Quarter Program on Heat Kernels, Random Walks, and Analysis on Manifolds and Graphs : April 16-July 13, 2002, Emile Borel Centre of the Henri Poincaré Institute, Paris, France

By: Pascal Auscher,T. Coulhon

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Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces

Lecture Notes from a Quarter Program on Heat Kernels, Random Walks, and Analysis on Manifolds and Graphs : April 16-July 13, 2002, Emile Borel Centre of the Henri Poincaré Institute, Paris, France

By: Pascal Auscher,T. Coulhon

This volume contains the expanded lecture notes of courses taught at the Emile Borel Centre of the Henri Poincare Institute (Paris). In the book, leading experts introduce recent research in their fields. The unifying theme is the study of heat kernels in various situations using related geometric and analytic tools. Topics include analysis of complex-coefficient elliptic operators, diffusions on fractals and on infinite-dimensional groups, heat kernel and isoperimetry on Riemannian manifolds, heat kernels and infinite dimensional analysis, diffusions and Sobolev-type spaces on metric spaces, quasi-regular mappings and $p$-Laplace operators, heat kernel and spherical inversion on $SL 2(C)$, random walks and spectral geometry on crystal lattices, isoperimetric and isocapacitary inequalities, and generating function techniques for random walks on graphs. This volume is suitable for graduate students and research mathematicians interested in random processes and analysis on manifolds.

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Page Count

434

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821833839

ISBN 13

9780821833834

Analysis and Geometry on Groups

By: Nicholas T. Varopoulos,L. Saloff-Coste,T. Coulhon

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Analysis and Geometry on Groups

By: Nicholas T. Varopoulos,L. Saloff-Coste,T. Coulhon

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.

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Page Count

172

Publisher

Cambridge University Press

Published Date

ISBN 10

0521353823

ISBN 13

9780521353823