-spaces, p≤1, and spline systems
Hajek-Renyi-type inequality for some nonmonotonic functions of associated random variables.
Hardy spaces for the Laplacian with lower order perturbations
We consider Hardy spaces of functions harmonic on smooth domains in Euclidean spaces of dimension greater than two with respect to the Laplacian perturbed by lower order terms. We deal with the gradient and Schrödinger perturbations under appropriate Kato conditions. In this context we show the usual correspondence between the harmonic Hardy spaces and the spaces (or the space of finite measures if p = 1) on the boundary. To this end we prove the uniform comparability of the respective harmonic...
Hardy-Littlewood theory on unimodular groups
Harmonic Analysis and nonstandard Brownian Motion in the plane.
Harmonic Analysis and Spectral Synthesis in Central Hypergroups.
Harmonic analysis of symmetric random graphs
This note attempts to understand graph limits as defined by Lovasz and Szegedy in terms of harmonic analysis on semigroups. This is done by representing probability distributions of random exchangeable graphs as mixtures of characters on the semigroup of unlabeled graphs with node-disjoint union, thereby providing an alternative derivation of de Finetti's theorem for random exchangeable graphs.
Harmonic analysis on fractal spaces
Harmonic ergodicity of actions of certain discrete linear groups
Harmonic functions along Brownan balls an the Liouville property for solvable Lie groups.
Harmonic functions and Hardy spaces on trees with boundaries
Harmonic functions on loop groups
Harmonic functions on multiplicative graphs and interpolation polynomials.
Harmonic measures for symmetric stable processes
Let D be an open set in ℝⁿ (n ≥ 2) and ω(·,D) be the harmonic measure on with respect to the symmetric α-stable process (0 < α < 2) killed upon leaving D. We study inequalities on volumes or capacities which imply that a set S on ∂D has zero harmonic measure and others which imply that S has positive harmonic measure. In general, it is the relative sizes of the sets S and that determine whether ω(S,D) is zero or positive.
Harmonic measures versus quasiconformal measures for hyperbolic groups
We establish a dimension formula for the harmonic measure of a finitely supported and symmetric random walk on a hyperbolic group. We also characterize random walks for which this dimension is maximal. Our approach is based on the Green metric, a metric which provides a geometric point of view on random walks and, in particular, which allows us to interpret harmonic measures as quasiconformal measures on the boundary of the group.
Harmonic spaces associated with parabolic and elliptic differential operators.
Harnack inequalities on graphs
Harnack inequality for functional sdes with bounded memory.
Harnack inequality for stable processes on d-sets
We investigate properties of functions which are harmonic with respect to α-stable processes on d-sets such as the Sierpiński gasket or carpet. We prove the Harnack inequality for such functions. For every process we estimate its transition density and harmonic measure of the ball. We prove continuity of the density of the harmonic measure. We also give some results on the decay rate of harmonic functions on regular subsets of the d-set. In the case of the Sierpiński gasket we even obtain the Boundary...
Hausdorff dimension of affine random covering sets in torus
We calculate the almost sure Hausdorff dimension of the random covering set in -dimensional torus , where the sets are parallelepipeds, or more generally, linear images of a set with nonempty interior, and are independent and uniformly distributed random points. The dimension formula, derived from the singular values of the linear mappings, holds provided that the sequences of the singular values are decreasing.