Full length article: Large subspaces of compositionally universal functions with maximal cluster sets

  • Authors:

  • L. Bernal-González;M. C. Calderón-Moreno;J. A. Prado-Bassas

  • Affiliations:

  • -;-;-

  • Venue:
  • Journal of Approximation Theory
  • Year:
  • 2012

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Abstract

Let (@f"n) be a sequence of holomorphic self-maps of a Jordan domain G in the complex plane. Under appropriate conditions on (@f"n), 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 a sequence of composition operators associated with (@f"n). Simultaneously, these functions also present maximal cluster sets along each member of a large class of curves in G tending to the boundary.