3 citations · 5 across the 5 of their papers we have counts for
5 papers
Dirichlet problems on graphs with ends
Tony Perkins
In classical potential theory, one can solve the Dirichlet problem on unbounded domains such as the upper half plane. These domains have two types of boundary points; the usual fin…
Convex and subharmonic functions on graphs
Matthew Burke, Tony Perkins
We explore the relationship between convex and subharmonic functions on discrete sets. Our principal concern is to determine the setting in which a convex function is necessarily s…
Non-compact versions of Edwards' Theorem
Nihat G. Gogus, Tony L. Perkins, Evgeny A. Poletsky
Edwards' Theorem establishes duality between a convex cone in the space of continuous functions on a compact space and the set of representing or Jensen measures for this cone. In…
Green functions, the fine topology and restoring coverings
Tony L. Perkins
There are several equivalent ways to define continuous harmonic functions on a compact set in . One may let be the unform closures of all functions i…
The Dirichlet Problem for Harmonic Functions on Compact Sets
Tony Perkins
For any compact set we develop the theory of Jensen measures and subharmonic peak points, which form the set , to study the Dirichlet problem…