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Random walks on co-compact fuchsian groups

Sébastien Gouëzel, Steven P. Lalley (2013)

Annales scientifiques de l'École Normale Supérieure

It is proved that the Green’s function of a symmetric finite range random walk on a co-compact Fuchsian group decays exponentially in distance at the radius of convergence R . It is also shown that Ancona’s inequalities extend to  R , and therefore that the Martin boundary for  R -potentials coincides with the natural geometric boundary S 1 , and that the Martin kernel is uniformly Hölder continuous. Finally, this implies a local limit theorem for the transition probabilities: in the aperiodic case, p n ( x , y ) ∼ C x , y R - n n - 3 / 2 .

Random walks on the affine group of local fields and of homogeneous trees

Donald I. Cartwright, Vadim A. Kaimanovich, Wolfgang Woess (1994)

Annales de l'institut Fourier

The affine group of a local field acts on the tree 𝕋 ( 𝔉 ) (the Bruhat-Tits building of GL ( 2 , 𝔉 ) ) with a fixed point in the space of ends ∂ 𝕋 ( F ) . More generally, we define the affine group Aff ( 𝔉 ) of any homogeneous tree 𝕋 as the group of all automorphisms of 𝕋 with a common fixed point in ∂ 𝕋 , and establish main asymptotic properties of random products in Aff ( 𝔉 ) : (1) law of large numbers and central limit theorem; (2) convergence to ∂ 𝕋 and solvability of the Dirichlet problem at infinity; (3) identification of the Poisson boundary...

Reducibility and unitary equivalence for a class of multiplication operators on the Dirichlet space

Yong Chen, Young Joo Lee, Tao Yu (2014)

Studia Mathematica

We consider the reducibility and unitary equivalence of multiplication operators on the Dirichlet space. We first characterize reducibility of a multiplication operator induced by a finite Blaschke product and, as an application, we show that a multiplication operator induced by a Blaschke product with two zeros is reducible only in an obvious case. Also, we prove that a multiplication operator induced by a multiplier ϕ is unitarily equivalent to a weighted shift of multiplicity 2 if and only if...

Regularity of some nonlinear quantities on superharmonic functions in local Herz-type Hardy spaces.

Dashan Fan, Shanzhen Lu, Dachun Yang (1998)

Publicacions Matemàtiques

In this paper, the authors introduce a kind of local Hardy spaces in Rn associated with the local Herz spaces. Then the authors investigate the regularity in these local Hardy spaces of some nonlinear quantities on superharmonic functions on R2. The main results of the authors extend the corresponding results of Evans and Müller in a recent paper.

Remarks on pluripolar hulls

Le Mau Hai, Nguyen Quang Dieu, Tang Van Long (2004)

Annales Polonici Mathematici

The aim of the paper is to establish some results on pluripolar hulls and to define pluripolar hulls of certain graphs.

Representation of functions by logarithmic potential and reducibility of analytic functions of several variables.

A. B. Sekerin (1996)

Collectanea Mathematica

The necessary and sufficient condition that a given plurisubharmonic or a subharmonic function admits the representation by the logarithmic potential (up to pluriharmonic or a harmonic term) is obtained in terms of the Radon transform. This representation is applied to the problem of representation of analytic functions by products of primary factors.

Resistance Conditions and Applications

Juha Kinnunen, Pilar Silvestre (2013)

Analysis and Geometry in Metric Spaces

This paper studies analytic aspects of so-called resistance conditions on metric measure spaces with a doubling measure. These conditions are weaker than the usually assumed Poincaré inequality, but however, they are sufficiently strong to imply several useful results in analysis on metric measure spaces. We show that under a perimeter resistance condition, the capacity of order one and the Hausdorff content of codimension one are comparable. Moreover, we have connections to the Sobolev inequality...

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