Rings of Meromorphic Functions

On the Configuration of Herman Rings of Meromorphic Functions

We prove some results concerning the possible configurations of Herman rings for transcendental meromorphic functions. We show that one pole is enough to obtain cycles of Herman rings of arbitrary period and give a sufficient condition for a configuration to be realizable.

Iteration of Meromorphic Functions

4. The Components of the Fatou set 4.1. The types of domains of normality 4.2. The classification of periodic components 4.3. The role of the singularities of the inverse function 4.4. The connectivity of the components of the Fatou set 4.5. Wandering domains 4.6. Classes of functions without wandering domains 4.7. Baker domains 4.8. Classes of functions without Baker domains 4.9. Completely in...

Rings of Analytic and Meromorphic Functionso)

Uniqueness of Meromorphic Functions∗

In this paper, Hinkkanen’s problem (1984) is completely solved, i.e., it is shown that any meromorphic function f is determined by its zeros and poles and the zeros of f (j) for j = 1, 2, 3, 4. To appear in J. Canad. Math. / Canad. J. Math.

Meromorphic Functions and Factoriality

Let K be a compact subset of a connected Stein manifold X. We study algebraic properties of the ring of meromorphic functions on X without poles in K.