2 research outputs found
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 also present maximal cluster sets along each member of a large class of curves in G tending to the boundary.Plan Andaluz de InvestigaciĂłn (Junta de AndalucĂa)Ministerio de Ciencia e InnovaciĂłnMinisterio de Ciencia y TecnologĂ