Lectures on complex approximation
Lectures on complex approximation
Journal of Approximation Theory
Multiply universal holomorphic functions
Journal of Approximation Theory
Hypercyclic sequences of differential and antidifferential operators
Journal of Approximation Theory
Holomorphic T-monsters and strongly omnipresent operators
Journal of Approximation Theory
Maximal cluster sets along arbitrary curves
Journal of Approximation Theory
Simultaneously maximal radial cluster sets
Journal of Approximation Theory
Simultaneously maximal radial cluster sets
Journal of Approximation Theory
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In this paper the new concept of totally omnipresent operators is introduced. These operators act on the space of holomorphic functions of a domain in the complex plane. The concept is more restrictive than that of strongly omnipresent operators, also introduced by the authors in an earlier work, and both of them are related to the existence of functions whose images under such operators exhibit an extremely wild behaviour near the boundary. Sufficient conditions for an operator to be totally omnipresent as well as several outstanding examples are provided. After extending a statement of the first author about the existence of large linear manifolds of hypercyclic vectors for a sequence of suitable continuous linear mappings, it is shown that there is a dense linear manifold of holomorphic monsters in the sense of Luh, so completing earlier nice results due to Luh and Grosse-Erdmann.