In this work we explore the relation between some local Dirichlet spaces and some operator ranges. As an application we give numerical bounds for an equivalence of norms on a particular subspace of the Hardy space. Based on these results we introduce an operator on H^2 which we study in some detail. We also ...
Combinatorial Games are a generalization of real numbers. Each game has a recursively defined complexity (birthday). In this paper we establish some game bounds. We find some limit cases for how big and how small a game can be, based on its complexity. For each finite birthday, N, we find the smallest positive ...