Harmonic Functions on Trees and Buildings
Will be published approx. on 30. June 1997
Book
Paperback/Softback
181 pages
978-0-8218-0605-0 (ISBN)
Description
This volume presents the proceedings of the workshop 'Harmonic Functions on Graphs' held at the Graduate Center of CUNY in the fall of 1995. The main papers present material from four minicourses given by leading experts: D. Cartwright, A. Figa-Talamanca, S. Sawyer and T. Steger. These minicourses are introductions which gradually progress to deeper and less known branches of the subject. One of the topics treated is buildings, which are discrete analogues of symmetric spaces of arbitrary rank; buildings of rank are trees. Harmonic analysis on buildings is a fairly new and important field of research.One of the minicourses discusses buildings from the combinatorial perspective and another examines them from the $p$-adic perspective. The third minicourse deals with the connections of trees with $p$-adic analysis. And the fourth deals with random walks, i.e., with the probabilistic side of harmonic functions on trees. The book also contains the extended abstracts of 19 of the 20 lectures given by the participants on their recent results. These abstracts, well detailed and clearly understandable, give a good cross-section of the present state of research in the field.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Weight
369 gr
ISBN-13
978-0-8218-0605-0 (9780821806050)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Classification
Content
Part 1. Minicourses: Local fields and trees by A. Figa-Talamanca Martin boundaries and random walks by S. A. Sawyer A brief introduction to buildings by D. I. Cartwright Local fields and buildings by T. Steger Part II. Abstracts of Lectures: Heat kernel for regular trees by D. Bednarchak Tensor product of spherical representations of the group of automorphisms of a homogeneous tree by D. I. Cartwright, M. G. Kuhn, and P. M. Soardi The horocyclic Radon transform on trees by E. C. Tarabusi Eigenfunctions of the Laplacian on a homogeneous tree by J. M. Cohen and F. Colonna Exotic convergence in theorems of Fatou type by F. Di Biase A spectral gap property for transfer operators by Y. Guivarclh Harmonic functions on discrete subgroups of semi-simple Lie groups by V. A. Kaimanovich Biased random walks and harmonic functions on the Lamplighter group by R. Lyons Characterization of the eigenfunctions of the Laplace operators for an affine building of rank 2 by A. M. Mantero and A. Zappa Free product of representations by W. Mlotkowski The Jacobian of a finite graph by T. Nagnibeda Flows and harmonic functions on graphs by S. Northshield Applications of diffusion processes on trees to mathematical finance by M. Pagliacci Characterizing harmonic functions by mean value properties on trees and symmetric spaces by M. A. Picardello Factors from buildings by J. Ramagge and G. Robertson Harnack and Liouville properties on graphs by M. Rigoli, M. Salvatori, and M. Vignati The spectrum of a directed Cayley graph of a free group by G. Robertson Factorization of the Green's kernel for non-nearest neighbor random walks by M. H. Taibleson Harmonic functions for group-invariant random walks by W. Woess.