Harmonic Analysis and Discrete Potential Theory

Front Matter....Pages i-viii
Compactifications Determined by a Polyhedral Cone Decomposition of ℝ n ....Pages 1-14
Maximal Functions at Infinity for Poisson Integrals on N A ....Pages 15-22
Potential at Infinity on Symmetric Spaces and Martin Boundary....Pages 23-46
On Rough Maximal Operators and Weak Type (1,1) Estimates for Convolutions....Pages 47-50
Laplace’s Method, Stationary Phase, Saddle Points, and a Theorem of Lalley....Pages 51-67
Besov Spaces on Non-Homogeneous Martingales....Pages 69-84
Boundary Representations of the Free Group, I....Pages 85-91
Boundary Representations of the Free Group, II....Pages 93-97
Negative Definite Kernels on Trees....Pages 99-105
Positive and Negative Definite Kernels on Trees....Pages 107-110
Probabilistic Methods for Ultracontractivity....Pages 111-129
Remarks on Amenability of Discrete Hypergroups....Pages 131-143
Measure-Theoretic Boundaries of Markov Chains, 0–2 Laws and Entropy....Pages 145-180
Perturbations of Operators, Connections with Singular Integrals, Hyperbolicity and Entropy....Pages 181-191
Isoperimetric Inequalities for Capacities....Pages 193-206
Sobolev Inequalities on Graphs and on Manifolds....Pages 207-214
Potential Theory on Non-Unimodular Groups....Pages 215-221
Harmonic Analysis of Random Walks on the Daisy Library Graph....Pages 223-232
The Rate of Escape of a Polynomial Random Walk on ℕ 2 ....Pages 233-247
Random Walks on ω -Networks....Pages 249-257
Trees, Ends, and Transience....Pages 259-266
On the Harmonic Measure of Self-Similar Sets on the Plane....Pages 267-280
Sharp Estimates for the Entropy....Pages 281-288
Asymptotic Properties of Unitary Representations of Tree Automorphisms....Pages 289-298
Back Matter....Pages 299-302