Radial limits of the Poisson kernel on the classical Cartan domains
Radial variation of functions in Besov spaces.
Random walks on co-compact fuchsian groups
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 . It is also shown that Ancona’s inequalities extend to , and therefore that the Martin boundary for -potentials coincides with the natural geometric boundary , and that the Martin kernel is uniformly Hölder continuous. Finally, this implies a local limit theorem for the transition probabilities: in the aperiodic case, .
Random walks on graphs with volume and time doubling.
This paper studies the on- and off-diagonal upper estimate and the two-sided transition probability estimate of random walks on weighted graphs.
Random walks on groups and monoids with a Markovian harmonic measure.
Random walks on the affine group of local fields and of homogeneous trees
The affine group of a local field acts on the tree (the Bruhat-Tits building of ) with a fixed point in the space of ends . More generally, we define the affine group of any homogeneous tree as the group of all automorphisms of with a common fixed point in , and establish main asymptotic properties of random products in : (1) law of large numbers and central limit theorem; (2) convergence to and solvability of the Dirichlet problem at infinity; (3) identification of the Poisson boundary...
Ray Processes on Locally Compact Spaces.
Ray sequences of Laurent-type rational functions.
Real analysis, quantitative topology, and geometric complexity.
In this paper, we give an overview of some topics involving behavior of homeomorphisms and ways in which real analysis can arise in geometric settings.
Real-Valued Duals of H-Cones.
Rearrangement estimates of the area integrals
We derive weighted rearrangement estimates for a large class of area integrals. The main approach used earlier to study these questions is based on distribution function inequalities.
Recherches axiomatiques sur le problème de Dirichlet
Recollement de semi-groupes de Feller locaux
Des semi-groupes de Feller locaux, deux à deux compatibles et définis sur des ouverts recouvrant un espace compact , se recollent en un semi-groupe de Feller local unique défini sur . Le principe du maximum joue un rôle essentiel dans la démonstration de ce résultat. Un théorème de recollement des générateurs infinitésimaux s’en déduit.
Rectifiability, analytic capacity, and singular integrals.
Rectilinearly and rectifiably ambiguous points of a function harmonic inside a sphere
Recurrence Criteria for Skew Products of Symmetric Markov Processes.
Reducibility and unitary equivalence for a class of multiplication operators on the Dirichlet space
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...
Refinement of an Lp-Estimate of Solonnikov for a Parabolic Equation of the Second Order with Conormal Boundary Condition.
Reflected double layer potentials and Cauchy's operators
Necessary and sufficient conditions are given for the reflected Cauchy's operator (the reflected double layer potential operator) to be continuous as an operator from the space of all continuous functions on the boundary of the investigated domain to the space of all holomorphic functions on this domain (to the space of all harmonic functions on this domain) equipped with the topology of locally uniform convergence.
Reflection and a mixed boundary value problem concerning analytic functions
A mixed boundary value problem on a doubly connected domain in the complex plane is investigated. The solution is given in an integral form using reflection mapping. The reflection mapping makes it possible to reduce the problem to an integral equation considered only on a part of the boundary of the domain.