Dirichlet finite harmonic measures on topological 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.

Topological Balls

Résumé. Cet article montre comment on peut utiliser la construction de Chu afin de simplifier la construction assez complexe de la catégorie ∗-autonome des boules qui sont réflexives et ζ-ζ∗-complètes donnée par le premier auteur dans les articles [Barr, 1976, 1979]. Abstract. This paper shows how the use of the “Chu construction” can simplify the rather complicated construction of the ∗-autono...

Harmonic Functions on Classical Rank One Balls

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...

Dirichlet Topological Defects

We propose a class of field theories featuring solitonic solutions in which topological defects can end when they intersect other defects of equal or higher dimensionality. Such configurations may be termed “Dirichlet topological defects”, in analogy with the D-branes of string theory. Our discussion focuses on defects in scalar field theories with either gauge or global symmetries, in (3+1) di...