Equivalence of domains with isomorphic semigroups of endomorphisms

@inproceedings{Merenkov2001EquivalenceOD,
  title={Equivalence of domains with isomorphic semigroups of endomorphisms},
  author={Sergei Merenkov},
  year={2001}
}
For two bounded domains Ω 1 , Ω 2 in C whose semigroups of analytic endomorphisms E(Ω 1 ), E(Ω 2 ) are isomorphic with an isomorphism φ: E(Ω 1 ) → E(Ω 2 ), Eremenko proved in 1993 that there exists a conformal or anticonformal map ψ: Ω 1 → Ω 2 such that φf = ψ o f o ψ -1 , for all f ∈ E(Ω 1 ). In the present paper we prove an analogue of this result for the case of bounded domains in C n . 

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References

SHOWING 1-10 OF 10 REFERENCES

On the characterization of a Riemann surface by its semigroup of endomorphisms

Suppose D 1 and D 2 be Riemann surfaces which have bounded nonconstant holomorphic functions. Denote by E(D i ), i = 1, 2, the semi-groups of all holomorphic endomorphisms. If φ: E(D 1 )→E(D 2 ) is

Functions conjugating entire functions toentire functions and semigroups of analytic endomorphisms

Answering two questions ot Rubei, we prove that there are unbounded plane domains which are notconformally or anticonformally equwalent but whose semigroups of analytic endomorphisms are isomorphic.

Function theory in several complex variables

Fundamental theory: Holomorphic functions and domains of holomorphy Implicit functions and analytic sets The Poincare, Cousin, and Runge problems Pseudoconvex domains and pseudoconcave sets

Hyperbolic complex spaces

1. Distance Geometry.- 2. Schwarz Lemma and Negative Curvature.- 3. Intrinsic Distances.- 4. Intrinsic Distances for Domains.- 5. Holomorphic Maps into Hyperbolic Spaces.- 6. Extension and Finiteness

Complex function theory

The first edition of this book appeared in 1963. The second edition contains additional exercises and new sections on convexity and complex numbers (transferred from Volume 2). The treatment is

Geometrical Methods in the Theory of Ordinary Differential Equations

Since the first edition of this book, geometrical methods in the theory of ordinary differential equations have become very popular and some progress has Since the author explains basic ideas free

On dimension theory

What do you do to start reading dimension theory? Searching the book that you love to read first or find an interesting book that will make you want to read? Everybody has difference with their

A survey of semigroups of continuous selfmaps

On the Meromorphic Function Field of a Stein Variety

47907 E-mail address: smerenko@math