Harmonic Analysis and Discrete Potential Theory

Compactifications Determined by a Polyhedral Cone Decomposition of ?n.- Maximal Functions at Infinity for Poisson Integrals on N A.- Potential at Infinity on Symmetric Spaces and Martin Boundary.- On Rough Maximal Operators and Weak Type (1, 1) Estimates for Convolutions.- Laplace’s Method, Stationary Phase, Saddle Points, and a Theorem of Lalley.- Besov Spaces on Non-homogeneous Martingales.- Boundary Representations of the Free Group, I.- Boundary Representations of the Free Group, II.- Negative Definite Kernels on Trees.- Positive and Negative Definite Kernels on Trees.- Probabilistic Methods for Ultracontractivity.- Remarks on Amenability of Discrete Hypergroups.- Measure-Theoretic Boundaries of Markov Chains, 0–2 Laws and Entropy.- Perturbations of Operators, Connections with Singular Integrals, Hyperbolicity and Entropy.- Isoperimetric Inequalities for Capacities.- Sobolev Inequalities on Graphs and on Manifolds.- Potential Theory on non Unimodular Groups.- Harmonic Analysis of Random Walks on the Daisy Library Graph.- The Rate of Escape of a Polynomial Random Walk on ?2.- Random Walks on ?-Networks.- ‘Trees, Ends, and Transience.- ‘On the Harmonic Measure of Self-Similar Sets on the Plane.- Sharp Estimates for the Entropy.- Asymptotic Properties of Unitary Representations of Tree Automorphisms.- Contributors.