The Martin Boundary for Harmonic Functions on Groups of Automorphisms of a Homogeneous Tree.
The Martin compactification of the Cartesian product of two hyperbolic spaces.
The Martin compactification of the polydisc at the bottom of the positive spectrum.
The Max-Plus Martin boundary.
Thinness and non-tangential limit associated to coupled PDE
In this paper, we study the reduit, the thinness and the non-tangential limit associated to a harmonic structure given by coupled partial differential equations. In particular, we obtain such results for biharmonic equation (i.e. ) and equations of type.
Transitions on a noncompact Cantor set and random walks on its defining tree
First, noncompact Cantor sets along with their defining trees are introduced as a natural generalization of -adic numbers. Secondly we construct a class of jump processes on a noncompact Cantor set from given pairs of eigenvalues and measures. At the same time, we have concrete expressions of the associated jump kernels and transition densities. Then we construct intrinsic metrics on noncompact Cantor set to obtain estimates of transition densities and jump kernels under some regularity conditions...