Rings of Analytic and Meromorphic Functions

Rings of Analytic and Meromorphic Functionso)

On Rings of Analytic Functions

Let D be a domain in the complex plane (Riemann sphere) and R(D) the totality of one-valued regular analytic functions defined in D. With the usual definitions of addition and multiplication R(D) becomes a commutative ring (in fact, a domain of integrity). A oneto-one conformai transformation f =0(z) of D onto a domain A induces an isomorphism ƒ—>ƒ* between R(D) and R(A):f(z) =ƒ*[(2)]. An an...

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.

Restricted Ideals in Rings of Analytic Functions

Introduction. Let Y be a connected, noncompact Riemann surface, and let A be the ring of all analytic functions on Y. It is known that the ideal theory of the ring A is strikingly similar to the ideal theory of the ring C(X) of all real valued continuous functions on a completely regular topological space X. We show that locally much of the ideal theory of A can be recovered from the ideal theo...

On Analytic Surfaces with Two Independent Meromorphic Functions.