Contemporary Mathematics 2003; 424 pp; softcover Volume: 338 ISBN10: 0821833839 ISBN13: 9780821833834 List Price: US$109 Member Price: US$87.20 Order Code: CONM/338
 This volume contains the expanded lecture notes of courses taught at the Emile Borel Centre of the Henri Poincaré 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 complexcoefficient elliptic operators, diffusions on fractals and on infinitedimensional groups, heat kernel and isoperimetry on Riemannian manifolds, heat kernels and infinite dimensional analysis, diffusions and Sobolevtype spaces on metric spaces, quasiregular 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. Readership Graduate students and research mathematicians interested in random processes and analysis on manifolds. Table of Contents  P. Auscher  Some questions on elliptic operators
 M. T. Barlow  Heat kernels and sets with fractal structure
 A. Bendikov and L. SaloffCoste  Brownian motions on compact groups of infinite dimension
 T. Coulhon  Heat kernel and isoperimetry on noncompact Riemannian manifolds
 B. K. Driver  Heat kernels measures and infinite dimensional analysis
 A. Grigor'yan  Heat kernels and function theory on metric measure spaces
 P. Hajłasz  Sobolev spaces on metricmeasure spaces
 I. Holopainen  Quasiregular mappings and the \(p\)Laplace operator
 J. Jorgenson and S. Lang  Spherical inversion on SL\(_2\)(C)
 M. Kotani and T. Sunada  Spectral geometry of crystal lattices
 V. Maz'ya  Lectures on isoperimetric and isocapacitary inequalities in the theory of Sobolev spaces
 S. Semmes  Some topics related to analysis on metric spaces
 K.T. Sturm  Probability measures on metric spaces of nonpositive curvature
 W. Woess  Generating function techniques for random walks on graphs
