Generalized cluster sets of real functions

Generalized Value Functions for Large Action Sets

The majority of value function approximation based reinforcement learning algorithms available today, focus on approximating the state (V) or state-action (Q) value function and efficient action selection comes as an afterthought. On the other hand, real-world problems tend to have large action spaces, where evaluating every possible action becomes impractical. This mismatch presents a major ob...

Real-variables characterization of generalized Stieltjes functions

We obtain a characterization of generalized Stieltjes functions of any order λ > 0 in terms of inequalities for their derivatives on (0,∞). When λ = 1, this provides a new and simple proof of a characterization of Stieltjes functions first obtained by Widder in 1938.

Cluster Sets of Functions Meromorphic in the Unit Circle.

Maximal cluster sets on spaces of holomorphic functions

In this paper, which has an expository nature, we consider the so called cluster sets, that is the set of accumulation points of the set of values taken by a (usually, holomorphic) function on prescribed subsets. We are specially interested in the action of holomorphic operators in order to obtain maximal cluster sets, see below for details. Extensions of classical cluster sets, where they are ...

Large subspaces of compositionally universal functions with maximal cluster sets

Let (φn) be a sequence of holomorphic self-maps of a Jordan domain G in the complex plane. Under appropriate conditions on (φn), we construct an H(G)-dense linear manifold –as well as a closed infinite-dimensional linear manifold– all of whose non-zero functions have H(G)-dense orbits under the action of the sequence of composition operators associated to (φn). Simultaneously, these functions a...