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Harmonic Functions on Trees and Buildings

Edited by: Adam Korányi City University of New York, Herbert H. Lehman College, Bronx, NY
Available Formats:
Softcover ISBN: 978-0-8218-0605-0
Product Code: CONM/206
181 pp
List Price: $49.00 MAA Member Price:$44.10
AMS Member Price: $39.20 Electronic ISBN: 978-0-8218-7797-5 Product Code: CONM/206.E 181 pp List Price:$46.00
MAA Member Price: $41.40 AMS Member Price:$36.80
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List Price: $73.50 MAA Member Price:$66.15
AMS Member Price: $58.80 Click above image for expanded view Harmonic Functions on Trees and Buildings Edited by: Adam Korányi City University of New York, Herbert H. Lehman College, Bronx, NY Available Formats:  Softcover ISBN: 978-0-8218-0605-0 Product Code: CONM/206 181 pp  List Price:$49.00 MAA Member Price: $44.10 AMS Member Price:$39.20
 Electronic ISBN: 978-0-8218-7797-5 Product Code: CONM/206.E 181 pp
 List Price: $46.00 MAA Member Price:$41.40 AMS Member Price: $36.80 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$73.50
MAA Member Price: $66.15 AMS Member Price:$58.80
• Book Details

Contemporary Mathematics
Volume: 2061997
MSC: Primary 31; Secondary 43; 60;

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. Figà-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.

Graduate students and research mathematicians interested in potential theory.

• Part I. Minicourses [ MR 1463725 ]
• Alessandro Figà-Talamanca - Local fields and trees [ MR 1463726 ]
• Stanley A. Sawyer - Martin boundaries and random walks [ MR 1463727 ]
• Donald I. Cartwright - A brief introduction to buildings [ MR 1463728 ]
• Tim Steger - Local fields and buildings [ MR 1463729 ]
• Part II. Abstracts of Lectures [ MR 1463725 ]
• Enrico Casadio Tarabusi - The horocyclic Radon transform on trees [ MR 1463732 ]
• Joel M. Cohen and Flavia Colonna - Eigenfunctions of the Laplacian on a homogeneous tree [ MR 1463733 ]
• Fausto Di Biase - Exotic convergence in theorems of Fatou type [ MR 1463734 ]
• Yves Guivarc’h - A spectral gap property for transfer operators [ MR 1463735 ]
• Vadim A. Kaimanovich - Harmonic functions on discrete subgroups of semi-simple Lie groups [ MR 1463736 ]
• Russell Lyons - Biased random walks and harmonic functions on the lamplighter group [ MR 1463737 ]
• A. M. Mantero and A. Zappa - Characterization of the eigenfunctions of the Laplace operators for an affine building of rank $2$ [ MR 1463738 ]
• Wojciech Młotkowski - Free product of representations [ MR 1463739 ]
• Tatiana Nagnibeda - The Jacobian of a finite graph [ MR 1463740 ]
• S. Northshield - Flows and harmonic functions on graphs [ MR 1463741 ]
• Mauro Pagliacci - Applications of diffusion processes on trees to mathematical finance [ MR 1463742 ]
• Massimo A. Picardello - Characterizing harmonic functions by mean value properties on trees on symmetric spaces [ MR 1463743 ]
• Jacqui Ramagge and Guyan Robertson - Factors from buildings [ MR 1463744 ]
• Marco Rigoli, Maura Salvatori and Marco Vignati - Harnack and Liouville properties on graphs [ MR 1463745 ]
• Guyan Robertson - The spectrum of a directed Cayley graph of a free group [ MR 1463746 ]
• Mitchell H. Taibleson - Factorization of the Green’s kernel for non-nearest neighbor random walks [ MR 1463747 ]
• Wolfgang Woess - Harmonic functions for group-invariant random walks [ MR 1463748 ]
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Volume: 2061997
MSC: Primary 31; Secondary 43; 60;

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. Figà-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.

Graduate students and research mathematicians interested in potential theory.

• Part I. Minicourses [ MR 1463725 ]
• Alessandro Figà-Talamanca - Local fields and trees [ MR 1463726 ]
• Stanley A. Sawyer - Martin boundaries and random walks [ MR 1463727 ]
• Donald I. Cartwright - A brief introduction to buildings [ MR 1463728 ]
• Tim Steger - Local fields and buildings [ MR 1463729 ]
• Part II. Abstracts of Lectures [ MR 1463725 ]
• Enrico Casadio Tarabusi - The horocyclic Radon transform on trees [ MR 1463732 ]
• Joel M. Cohen and Flavia Colonna - Eigenfunctions of the Laplacian on a homogeneous tree [ MR 1463733 ]
• Fausto Di Biase - Exotic convergence in theorems of Fatou type [ MR 1463734 ]
• Yves Guivarc’h - A spectral gap property for transfer operators [ MR 1463735 ]
• Vadim A. Kaimanovich - Harmonic functions on discrete subgroups of semi-simple Lie groups [ MR 1463736 ]
• Russell Lyons - Biased random walks and harmonic functions on the lamplighter group [ MR 1463737 ]
• A. M. Mantero and A. Zappa - Characterization of the eigenfunctions of the Laplace operators for an affine building of rank $2$ [ MR 1463738 ]
• Wojciech Młotkowski - Free product of representations [ MR 1463739 ]
• Tatiana Nagnibeda - The Jacobian of a finite graph [ MR 1463740 ]
• S. Northshield - Flows and harmonic functions on graphs [ MR 1463741 ]
• Mauro Pagliacci - Applications of diffusion processes on trees to mathematical finance [ MR 1463742 ]
• Massimo A. Picardello - Characterizing harmonic functions by mean value properties on trees on symmetric spaces [ MR 1463743 ]
• Jacqui Ramagge and Guyan Robertson - Factors from buildings [ MR 1463744 ]
• Marco Rigoli, Maura Salvatori and Marco Vignati - Harnack and Liouville properties on graphs [ MR 1463745 ]
• Guyan Robertson - The spectrum of a directed Cayley graph of a free group [ MR 1463746 ]
• Mitchell H. Taibleson - Factorization of the Green’s kernel for non-nearest neighbor random walks [ MR 1463747 ]
• Wolfgang Woess - Harmonic functions for group-invariant random walks [ MR 1463748 ]
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