Existence of Dirichlet finite harmonic measures on Euclidean balls

Rough Isometries and Dirichlet Finite Harmonic Functions on Graphs

Suppose that G\ and G% are roughly isometric connected graphs of bounded degree. If G\ has no nonconstant Dirichlet finite harmonic functions, then neither has Gi.

Extremal Positive Pluriharmonic Functions on Euclidean Balls

Contrary to the well understood structure of positive harmonic functions in the unit disk, most of the properties of positive pluriharmonic functions in symmetric domains of C, in particular the unit ball, remain mysterious. In particular, in spite of efforts spread over quite a few decades, no characterization of the extremal rays in the cone of positive pluriharmonic functions in the unit bal...

An extension theorem for finite positive measures on surfaces of finite‎ ‎dimensional unit balls in Hilbert spaces

A consistency criteria is given for a certain class of finite positive measures on the surfaces of the finite dimensional unit balls in a real separable Hilbert space. It is proved, through a Kolmogorov type existence theorem, that the class induces a unique positive measure on the surface of the unit ball in the Hilbert space. As an application, this will naturally accomplish the work of Kante...

Tolerant identification with Euclidean balls

The concept of identifying codes was introduced by Karpovsky, Chakrabarty and Levitin in 1998. The identifying codes can be applied, for example, to sensor networks. In this paper, we consider as sensors the set Z 2 where one sensor can check its neighbours within Euclidean distance r. We construct tolerant identifying codes in this network that are robust against some changes in the neighbourh...

Harmonic Functions on Classical Rank One Balls