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
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Bibliographic Information
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
（Contemporary mathematics, 338）
American Mathematical Society, c2003
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC22:515.353/AU722070601064
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Includes bibliographical references
Description and Table of Contents
Description
This volume contains the expanded lectures 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.
Table of Contents
Some questions on elliptic operators by P. Auscher Heat kernels and sets with fractal structure by M. T. Barlow Brownian motions on compact groups of infinite dimension by A. Bendikov and L. Saloff-Coste Heat kernel and isoperimetry on non-compact Riemannian manifolds by T. Coulhon Heat kernels measures and infinite dimensional analysis by B. K. Driver Heat kernels and function theory on metric measure spaces by A. Grigor'yan Sobolev spaces on metric-measure spaces by P. Hajlasz Quasiregular mappings and the $p$-Laplace operator by I. Holopainen Spherical inversion on SL$_2$(C) by J. Jorgenson and S. Lang Spectral geometry of crystal lattices by M. Kotani and T. Sunada Lectures on isoperimetric and isocapacitary inequalities in the theory of Sobolev spaces by V. Maz'ya Some topics related to analysis on metric spaces by S. Semmes Probability measures on metric spaces of nonpositive curvature by K.-T. Sturm Generating function techniques for random walks on graphs by W. Woess.
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