CURVILINEAR CLUSTER SETS OF ARBITRARY FUNCTIONS

Maximal cluster sets of L-analytic functions along arbitrary curves

Let Ω be a domain in the N -dimensional real space, L be an elliptic differential operator, and (Tn) be a sequence whose members belong to a certain class of operators defined on the space of L-analytic functions on Ω. It is proved in this paper the existence of a dense linear manifold of L-analytic functions all of whose nonzero members have maximal cluster sets under the action of every Tn al...

Maximal cluster sets along arbitrary curves

The existence of a dense linear manifold of holomorphic functions on a Jordan domain having except for zero maximal cluster set along any curve tending to the boundary with nontotal oscillation value set is shown.

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...