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Winding of geodesic rays chosen by a harmonic measure
We prove limit theorems for the homological winding of geodesic rays distributed via a harmonic measure on a Gromov hyperbolic space. We obtain...
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Linear measure of non-iterative dynamic system of harmonic functions
The main purpose of this paper is to determine the linear measure of non-iterative dynamic system of some classes of harmonic functions.
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Absolute Continuity of the Harmonic Measure on Low Dimensional Rectifiable Sets
In the past decades, we learnt that uniform rectifiability is often a right candidate to go past Lipschitz boundaries in boundary value problems. If
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Harmonic Measure of Arcs of Fixed Length
We consider Jordan domains Ω with piece-wise smooth boundaries such that all arcs α ⊂ ∂Ω having fixed length l, 0 < l < length(∂Ω), have equal...
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Boundary behavior of harmonic functions on metric measure spaces with non-negative Ricci curvature
Let ( X, d, μ ) be a metric measure space with non-negative Ricci curvature. This paper is concerned with the boundary behavior of harmonic function on...
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Geometric Harmonic Analysis III Integral Representations, Calderón-Zygmund Theory, Fatou Theorems, and Applications to Scattering
This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate...
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Geometric Harmonic Analysis IV Boundary Layer Potentials in Uniformly Rectifiable Domains, and Applications to Complex Analysis
This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate...
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Geometric Harmonic Analysis V Fredholm Theory and Finer Estimates for Integral Operators, with Applications to Boundary Problems
This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate...
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A harmonic property of right invariant priors
It is shown that, on any Lie group, the density ratio of the right invariant measure to the left invariant measure is harmonic with respect to the...
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Subclasses of Harmonic Functions with Nonnegative Harmonic Majorants in the Halfplane
In this chapter, we consider some \(\omega \)...
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Groups, Drift and Harmonic Measures
In this short note we will describe an old problem and a new approach which casts light upon it. The old problem is to understand the nature of...
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Bounded harmonic maps
The classical Fatou theorem identifies bounded harmonic functions on the unit disk with bounded measurable functions on the boundary circle. We...
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Harmonic Measures and Numerical Computation of Cauchy Problems for Laplace Equations
It is well known that the Cauchy problem for Laplace equations is an ill-posed problem in Hadamard’s sense. Small deviations in Cauchy data may lead...
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Geometric Harmonic Analysis I A Sharp Divergence Theorem with Nontangential Pointwise Traces
This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate...
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Asymptotically Mean Value Harmonic Functions in Subriemannian and RCD Settings
We consider weakly and strongly asymptotically mean value harmonic (amv-harmonic) functions on subriemannian and RCD settings. We demonstrate that,...
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Geometric Harmonic Analysis II Function Spaces Measuring Size and Smoothness on Rough Sets
This monograph is part of a larger program, materializing in five volumes, whose principal aim is to develop tools in Real and Harmonic Analysis, of...
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Markov Chains and Harmonic Functions
The study of transient random walks is inextricably tied to the theory of harmonic functions for the step distribution, as these functions determine...